I was just on holiday in south eastern Europe in a resort town where the workforce was entirely composed of the same kind of immigrants, and none of these immigrants were "integrated" by this standard. But there was no criminality. Maybe because all of them were gainfully employed and felt like they had a future.
That's just one example.
My point is, there is a false equivalence being exercised here. Just because somebody is not integrated by whatever arbitrary standard, does not mean that they are prone to engage in criminal activity.