Huntsman, 39, told police she did not kill a seventh infant which was stillborn also found hidden in the garage, the affidavit adds.
The grisly case was publicly unveiled by police on Sunday after Huntsman was arrested on suspicion of six counts of first-degree felony murder.
On Monday morning, via closed-circuit TV from the Utah County jail, Huntsman appeared in 4th District Court, where bail was set at $6 million.
Huntsman, wearing a worn blue jumpsuit with the sleeves rolled up to her shoulders, appeared tired during the hearing.
As she stepped in front of the camera, she pressed her hand to her face, covering her eyes. Seconds later when prosecutors asked for a $6 million bail, Huntsman merely blinked and showed no perceptible emotion.
"That's fine," she told Judge Steven Hansen blankly when he asked her what she thought of the massive sum.
Huntsman has been on suicide watch ever since she was booked into the jail, said Utah County Sheriff's Chief Deputy Darin Durfey.
Utah County Attorney Jeff Buhman said Huntsman will be back in court April 21, which is likely the earliest date that charges would be filed.
Buhman explained the high, cash-only bail by saying that Huntsman is a "flight risk and because this is a heinous, horrible crime."
Buhman added: "This is a little shocking because of the number of babies that were killed."
Pleasant Grove detective Dan Beckstrom said after the hearing: "I've never seen anything like this in my career."
The seven infants, all in their own boxes, were inside a cabinet amid other boxes and items, added Pleasant Grove Police Chief Michael Smith.
The arrest affidavit said Huntsman told the police, after waiving her Miranda rights, that she gave birth to the seven babies at her Pleasant Grove home between 1996 and 2006. She also told police that she strangled or suffocated the babies immediately after they were born, the affidavit adds.
Investigators found each baby wrapped in a towel or shirt, and placed inside a plastic bag, and each was in a separate cardboard box, according to the affidavit.
Police said Huntsman has not lived at the home since 2011.
Huntsman's alleged secret was exposed when her estranged husband, 41-year-old West, found one of the dead infants while cleaning out the garage at the home on Saturday. West contacted Huntsman, who admitted the baby was hers, and had been stillborn in 2006, the arrest affidavit states.
West then called police, according to the affidavit.
Police obtained a search warrant and found six more babies packaged in separate cardboard boxes inside the garage, said Pleasant Grove police Capt. Michael Roberts.
The state Medical Examiner's Office has examined the infants, but is bringing in a specialist before completing its report, Smith said. The police chief said he hopes to identify the genders of all seven, but added that, for now, decomposition makes that difficult.
At first glance, all the babies appear to be full term, Smith said.
Huntsman who was contacted by police at her West Valley City residence, where she had moved agreed to go with officers to the Pleasant Grove police station, where she allegedly admitted to the homicides.
Residents of the neighborhood called Huntsman a great neighbor. One neighbor had even trusted Huntsman to watch her grandson.
Huntsman's estranged husband is believed to be the father of the dead babies, but investigators are still working on DNA tests, Roberts said. Police also are looking into how much knowledge, if any, West had of the pregnancies. But at this point they are not pursuing charges against him.
West has not lived in the home for several years. In 2006, he was sentenced to prison on state and federal drug convictions and is currently residing in a Salt Lake County halfway house. His release date is July 10.
According to a statement in advance of plea filed in U.S. District Court, West admitted that between August 2002 and April 2005, he bought pints of iodine online that were used to manufacture methamphetamine. Police officers also found 199 matchbook striker plates with phosphorous extracted from them in the garbage at the man's Pleasant Grove home, according to court records.
West pleaded guilty in federal court in August 2006 to two counts of possession of a controlled substance and was sentenced to 108 months in federal prison.
Also in August 2006, West pleaded guilty in state court to one count of illegal possession or use of a controlled substance, a third-degree felony, along with misdemeanor DUI. He was given a zero-to-five-years prison sentence, which was ordered to run concurrent with his federal sentence.
Huntsman wrote a letter to the federal judge in July 2006 in which she asked for lenience at her husband's sentencing. Also in the letter, she said she had allowed a search of her home by two Drug Enforcement Administration agents, who apparently did not find the dead babies.
"We need this guy to keep our family together," Huntsman wrote of her husband. "Everybody loves this guy."
Letters from other family members of Huntsman and West painted a picture of a close-knit, loving family who enjoyed camping, fishing and spending time together. West was the sole provider for the family, according to the letters, and worked for several years at an excavation company.
"Darren has always spent quality time with his wife, Megan, and his three daughters," his mother, Diane West, wrote in a letter. "The girls love their dad."
West's family has issued a statement saying they are in a "state of shock and confusion."
"We are mourning this tragic loss of life and we are trying to stay strong and help each other through this awful event," the statement said before asking for privacy.
Longtime neighbor Sharon Chipman said West's parents own the home where the dead babies were discovered, and that Huntsman's three daughters still live there. The eldest daughters are around 18 to 20 years old, while the youngest is now about 13, Chipman said.
The youngest daughter would have been born in the middle of the time when Huntsman was allegedly killing the infants, which raises questions for the police about why that girl was allowed to live, the police chief said.
West had been cleaning out the garage Saturday because he was getting ready to move back into the house this summer, Chipman said.
Chipman had noticed that Huntsman had gained and lost some weight in the years she lived there, but Chipman never considered that she was pregnant.
She was a great neighbor, and Chipman said she trusted Huntsman to watch her grandson, when he was a toddler, for years.
Aaron and Kathie Hawker live next door to the house and have known the family for years. Aaron Hawker said Saturday he had been watching police come and go from the house all day, adding that he never thought Huntsman looked pregnant.
He also described her as a great neighbor, and her husband as "a good guy."
The Hawkers said Huntsman moved out several years ago, leaving her three daughters to live alone.
"It makes us so sad, we want to cry," Kathie Hawker said of the alleged homicides and Huntsman's arrest. "We enjoyed having them as a neighbor. This has just blown us away."
The girls were normal youngsters, coming and going often, neighbor Vickie Nelson said.
"It's shocking and kind of morbid and strange," Nelson said as she looked across the street at the garage from her from lawn.
Like others in the Pleasant Grove area, Sandee Wall also said Huntsman was a good neighbor who was "very quiet."
Wall described Huntsman's three daughters as "fun loving." The daughters are now staying with grandparents, Wall said.
Wall added that Huntsman seemed to have a drinking problem, which may have led to Huntsman being asked to move from the Pleasant Grove home.
Police captain Roberts said the case has been "emotionally draining" and upsetting to investigators. He was at the home when the bodies were discovered.
"My personal reaction? Just shocked. Couldn't believe it. The other officers felt the same," the 19-year police veteran said. "They got more and more shocked each box they opened."
Huntsman has no criminal record, aside from a 2011 traffic citation, according to a search of Utah court records.
The Associated Press contributed to this story.
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Safe Haven law enacted to save babies' lives
Utah has had a Safe Haven law on the books since 2001, allowing biological parents to anonymously give up custody of their newborn child without facing any legal consequences. Intended to save children's lives, the law tries to prevent women from abandoning infants in places such as trash cans and bathrooms.
The hotline is open 24 hours a day, every day of the week. For more information, go to utahsafehaven.org or follow them on Twitter at twitter.com/UtahNewborn.