In which year was female boxing formally integrated into the official medal events of the Summer Olympic Games for the very first time?

The correct option is 2012.

Female boxing was formally integrated into the official medal events of the Summer Olympic Games for the very first time at the 2012 London Olympic Games.
While men's boxing had been included in the Olympic program since 1904, women's boxing was officially approved for inclusion by the Executive Board of the International Olympic Committee (IOC) in 2009, making its official debut at the 2012 Games in London with competition across three weight classes: flyweight, lightweight, and middleweight.