I think things work best when there is a dominant culture which is confident and secure enough in itself to make space for minority cultures, and those minority cultures have to encourage the competence of their members in the majority culture, and accept that it is the dominant culture. Of course, this is exactly what most minorities do. That's what I would understand by integration. Certainly not a one-size fits-all complete melting pot. That works when there is cultural closeness and a fast growing economy which people want to be part of in the first place eg the 19th century US immigration experience. Dominant cultures do shift a bit like the Theseus ship or old broom/new broom paradox -but they don't shift as much or as quickly as large scale population movements require them to do. In fact a map of the basic world culture groups is one characterized by stability than change even today.
I'm pessimistic about multi-cultural, all-cultures-are-equal approaches. For one thing, they aren't. For all the evils of liberal imperialism and its successors, they hold up well in a comparative dominant cultures competition. Ask yourself in which other cultures would this discussion be taking place. And besides, while I have no interest in exporting liberalism's culture to other places and people, it suits me and mine.
It is not enough to say one man's terrorist is another man's freedom fighter. We have to exercise our judgement on the positions we think people occupy on the terrorist-patriot continuum. The French resistance was different from Hamas, and Israel is different from its neighbors. In their imperfect ways, they are both working towards widening freedom -even if the former sometimes played roulette with its own compatriots taken hostage by the Germans, and even if
the latter thinks that history has given it a huge credit in its moral bank account which allows it to cut corners. I think Hamas and the IRA are closer to protection rackets exploiting the misery and frustration of people.
Nor is it good enough to focus merely on the people who exploit division.s It is true that people do this and it is true that they are a problem. However, this can be a form of deflection, especially when it implies that the divisions would not be there except for bad people stirring them up to distract from other sources of discontent.
The track record of political communities where there is any thing close to a balance of power or numbers -Yugoslavia, Lebanon, maybe even Belgium, is not good -and even where there is a large minority there is difficulty. If I were to be optimistic, I'd look at Canada as a pretty good story. Managing the French fact has become a way of life, rather than a question to be resolved. Attitudes to very large numbers of immigrants from all over the place remain positive. Even so, Canada has wealth and space, and there are signs that it has limits, even if they remain far off for now.