Challenge Problems:
EDIT: I don't like the second integral. It doesn't even make any sense unless you state that is a real-valued function. Sorry. It's a bad problem.
Moderator edit: Approved Challenge question.
Nice.
If for the first integral you made the same substitution but didn't break it up into two integrals, you would get I = -I.
And for the second integral, Maple claims the answer is a complex number and Mathematica doesn't know what to do with it. The issue is the cube root of negative real numbers.