If we have:
Let $I := [a,b]$ and let $f: I\to\mathbb ℝ$ be continuous on $I$. Also let $J := [c,d]$ and let $u: J\to\mathbb ℝ$ be differentiable on $J$ and satisfy $u(J)\subseteq I$. Show that if $G: J\to\mathbb ℝ$ is defined by $ G(x) :=\int_a^{u(x)} f(t)\,dt $ for $x$ in $J$, then $G'(x) = (f \circ u)(x)u'(x)$ for all $x\in J$.
Can we just say use the Fundamental Thm of Calculus or do we need to break it up over two integrals?