As correctly stated, A and B are good because they both equal to 0, soo they are ruled out.
C fails because by taking the odd function f(x) = -x^3, we have
\begin{align*} &\quad\int_{-a}^0 f(x)\,dx + \left| \int_0^a f(x)\,dx \right|\\ &= \int_{-a}^0 -x^3\,dx + \left| \int_0^a -x^3\,dx...