Visual Calculus - Fundamental Theorem of Calculus

Problem:
Investigate whether the program Maple "knows" the Fundamental Theorem of Calculus.

Visualization:
Consider the following code:

> F:=x->int(f(t),t=a..x);

> diff(F(x),x);

> G:=x->diff(g(x),x);

> int(G(x),x=a..b);