Do you have to change limits of integration when you use substitution

I can clarify further if need be.

Yes and No.

When you use a substitution (say u= x+1, when x varies from 0 to 1), you can evaluate integral in two ways

1) change integral limits to u (u varies from 1 to 2) and evaluate for u.
2) calculate integral and sub back u with x and evaluate for x (in this case you dont need to change the limits)