Integration is more than a bringing together: it the uniting of parts into a new whole. It is used to describe the goal of psychological development in Jungian Psychology culminating in the person actually becoming the Higher Self rather than the personality.
It is a difficult concept because it is a change of identity from the "I" of the personality into a new "I" that incorporates the transformed elements of the old personality into a new Whole Person centered on the Higher Self.
As a result of this type of psychological work, the question "Who am I?" requires a new answer.