$\begin{align*} \int_0^{\pi} x f (\sin x ) dx \end{align*}$ is equal to :

Question

( A ) $ \begin{align*} \frac{\pi}{2} \int_0^{\frac{\pi}{2} }f(\sin x) dx \end{align*}$
( B ) $ \begin{align*} \pi \int_0^{\pi}f(\sin x) dx \end{align*}$
( C ) $ \begin{align*} \pi \int_0^{\pi}f(\cos x) dx \end{align*}$
( D ) $ \begin{align*} \pi \int_0^{\frac{\pi}{2} }f(\cos x) dx \end{align*}$