Originally Posted by

**kaiser0792** But my problem is that when the book was teaching u-substitution, I understood that unless limits of integration were changed that the final answer would have to be changed back in terms of x. However, in the chapter on integration of inverse trig functions, the book uses u-substitution but doesn't change the limits of integration in terms of u and just integrates as if the integral was written in terms of x. So how is it that in some instances, u-substitution warrants changes in limits of integration, and in other instances, u-substitution is used but the limits of integration are not changed to compensate for the u-substitution?