I don't think it's reasonable to "demand" integration. What should happen is that the existing cultures should be open and welcoming enough so that new-comers want to take part. Also, I like the idea of immigrants bringing their culture with them (and in some cases, that may be the last representation of that culture) and welcoming people to learn about it.
Multi-culturalism should be about championing different cultures and not forcing everyone into a cultural homogeneity.
Multi-culturalism should be about championing different cultures and not forcing everyone into a cultural homogeneity.