Washington (CNN) On the day that President Donald Trump announced the death of Abu Bakr al-Baghdadi, the parents of Kayla Mueller, who was kidnapped and reportedly raped by the ISIS leader, say they are feeling a "roller coaster of emotions."

"Well, it's a roller coaster of emotions whenever this ugly situation raises its head, but it's become part of our life over the last five and a half years," Kayla's father Carl Mueller told CNN in a phone interview Sunday afternoon.

In 2012, Kayla traveled to the Turkey/Syria border to work with the Danish Refugee Council and the humanitarian organization Support to Life, which assisted families forced to flee their homes. She was taken hostage by ISIS in Aleppo, Syria, in 2013 after she visited a Spanish MSF (Doctors Without Borders) hospital. The family confirmed Kayla's death in 2015 but her body has not been recovered.

Carl and Marsha Mueller said they were at home in Prescott, Arizona, on Saturday when they were messaged by a reporter about the possibility that Baghdadi may have been killed. Marsha said her first reaction to the news was uncertainty, because of the previous times the ISIS leader was believed to have been killed.

The Muellers received the official confirmation of Baghdadi's death in listening to Trump's news conference Sunday morning. They praised and thanked the President, the US military and special forces for taking action.

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