JEE Math Practice Question

For $$x \in \left( {0,{{5\pi } \over 2}} \right),$$ define $$f\left( x \right) = \int\limits_0^x {\sqrt t \sin t\,dt.} $$ Then $$f$$ has

1. A.local minimum at $$\pi $$ and $$2\pi $$
2. B.local minimum at $$\pi $$ and local maximum at $$2\pi $$
3. C.local maximum at $$\pi $$ and local minimum at $$2\pi $$
4. D.local maximum at $$\pi $$ and $$2\pi $$