If $$g(x) = \int_{\sin x}^{\sin(2x)} \sin^{-1}(t)dt$$ then

A

$$g'(\frac{\pi}{2})=-2\pi$$

B

$$g'(-\frac{\pi}{2})=2\pi$$

C

$$g'(\frac{\pi}{2})=2\pi$$

D

$$g'(-\frac{\pi}{2})=-2\pi$$