I've been doing some Quantum mechanics problems, and a great number of them use the fact that a integrand is odd to find <x> to be zero.

Anyways, for this kind of integrand:

X*(sin^2(n*pi*x)) , i see that they do not use the odd integrand argument, and do not get zero as an answer.

Why is it that we cant use that trick here? (sorry for my rusty calculus)