For $$x \in \left(0, \dfrac{5\pi}{2}\right)$$, define $$f(x) = \displaystyle \int_0^x \sqrt{t} \sin t \, dt$$. Then $$f$$ has:

A

local minimum at $$\pi$$ and $$2\pi$$

B

local minimum at $$\pi$$ and local maximum at $$2\pi$$

C

local maximum at $$\pi$$ and local minimum at $$2\pi$$

D

local maximum at $$\pi$$ and $$2\pi$$