If someone integrates into a social group, or is integrated into it, they behave in such a way that they become part of the group or are accepted into it.
When races integrate or when schools and organizations are integrated, people who are black or belong to ethnic minorities can join white people in their schools and organizations.
If you integrate one thing with another, or one thing integrates with another, the two things become closely linked or form part of a whole idea or system. You can also say that two things integrate .