## Calculus (3rd Edition)

We know that for any odd function $f(x)$, the integral $\int_{-a}^af(x)dx=0$. Now, since $xy^2$ and $\sin x$ are odd functions in $x$ and $x$ changes from $-1$ to $1$, then the integrals that will be zero are (b) and (c). The function in (d) is not odd and the function in (a) is not odd over $x$.