My T has never used the word integration with me so I don't really know much about that. We have been practicing having meetings and talking to each other and learning about each others needs and point of view though and that seems to help us a lot. Each time we talk with one and come to understand their job and how they do it and how they are actually trying to help the system overall it seems to change things inside and make it better or easier somehow. Even though my T hasn't discussed "integration" with us it feels to me like it would be something like that. Talking sharing understanding helping supporting knowing caring accepting cooperating.
I suppose different therapists with different training have different ideas and opinions about integration. The closest thing i have seen like a "how to" guide for treating DID is from a site called ISSTD, they have therapy guidelines for treating DID, but I think even they don't mention "integration". I'm not sure.