Answer
$F'(x)=\sqrt {\sin (x)}\times\cos (x)$
Work Step by Step
$F(x)=\int_0^{\sin(x)}(\sqrt t){dt}$
$F'(x)=\frac{d}{dx}(\int_0^{\sin(x)}(\sqrt t){dt})$
$=\frac{d}{dx}(\int_0^{u(x)}(\sqrt t){dt})$, where $u(x)=\sin (x)$
$=\frac{d}{dx}(\int_0^{u}(\sqrt t){dt})\times\frac{du}{dx}$, using the Chain Rule
$=\sqrt {\sin (x)}\times\cos (x)$
