Deriving a function inside an integral I have to derive the following function
$\frac{d\int f(x(t))dt}{dx}$ =$f'(x(t))$
Can someone explain me why I can ignore the integral? Is there a theorem that says so?
thank you! 
EDIT (by mickep)
Here is a scanned snippet of page 55, equation (2.16) and (2.17) in the book mentioned in the comments. I think it might be helpful for everyone to see. I don't see how that fit the question asked, though.


The definition of the indefinite integral is that it is the anti derivative of the integrand. Precisely that if $F(x)=\int f(x) dx$ then $F'(x)=f(x)$
The fundamental theorem of calculus tells us that if $F(x)=\int_a^x f(t)dt$ then $F'(x)=f(x)$
