Exercise 17, § 1

Let $g$ be a real function admitting a continuous derivative, and $\neq 0$ on $[a, x]$; if $f$ is a real function having a regulated $(n+1)^{th}$ derivative on $[a, x]$, show that the remainder $r_n(x)$ in the Taylor expansion of order $n$ for $f$ at the point $a$ can be written

where $a < \xi < x$ (use the integral form for $r_n(x)$).