MHB Find the derivative of the antiderivative

[Umar]

I know it seems pretty self explanatory, but I've tried to do this question and I've apparently gotten the wrong answer twice.

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If anyone can give me a clear solution to the problem, that would be greatly aooreciated. I initially tried to follow a video I saw online, but I think there is something different I need to do considering the bounds. Maybe splitting the integral?

 

[MarkFL]

By the FTOC and the Chain Rule, we have:

$$\frac{d}{dx}\int_{g(x)}^{h(x)} f(t)\,dt=f(h(x))\frac{dh}{dx}-f(g(x))\frac{dg}{dx}$$

Can you use this rule to compute $F'(x)$?