Math Help - Deriving defined Integral

1. Deriving defined Integral

I need to derive defined integral which does look like this...

$F(x)=\int_0^x{\frac{\cos t}{1+t^2}dt}$

$F'(x)=?$

2. See attachment

3. Thankyou...

how can i get left and right limit of this derivate function?

$\frac{dF}{dx}=F'(x)=\frac{\cos t}{1+t^2}$

4. Not not quite right

F ' (x) = cos(x)/(1+x^2) here we have x not t

5. Forgot to change t to x thankyou.