Quote Originally Posted by I Took the Red Pill View Post
F(x)= ∫ F(t) dt on the interval [c,x²], correct?

F'(x) = 2xF(x)

F(x) ≠ 2xF(x)

The Second Fundamental Theorem of Calculus allows you to do what you did to find the derivative of the anti-derivative of the function with respect to x, not the integral. So the way you phrased it, no.
Oh yes, yes. I see.