For $x \in (0, \frac{5 \pi}{2})$, define $f(x) = \int_0^x \;\sqrt{t} \;\sin t \;dt$. Then $f$ has

Question

( A ) local maximum at $\pi$ and $2 \pi$
( B ) local maximum at $\pi$ and local minimum at $2 \pi$
( C ) local minimum at $\pi$ and $2 \pi$
( D ) local minimum at $\pi$ and local maximum at $2 \pi$