Is this true about integrating composite functions? Let's say that I'm integrating a composite function, say $f(g(x))$, that is in a form to which I can apply the substitution rule.  Is it true to say that both $f$ and $g$ must be differentiable?
I understand that the substitution rule requires $g$ to be differentiable and that the substitution rule relies on the chain rule, and the chain rule requires both f and g to be differentiable.

if you talk about the Riemann-integral: if $f : [a,b] \to [c,d]$ R-integrable and $g : [c,d] \to \mathbb{R}$ continuous, than $g \circ f : [a,b] \to \mathbb R$ is R-integrable.
Differentiable implies continuous, so if f,g are differentiable they are R-integrable
