Integrability of composite functions

Question

Let $f$ be a Riemann-integrable function on a closed interval $[a,b] \subset \mathbb{R}$. Let g be a function on $\mathbb{R}$. What conditions must g satisfy so that $g \circ f$ is also Riemann-integrable ? Thank you!

Answer 1

See this post Riemann Integrability of Compositions

If $f$ is a Riemann integrable function defined on $[a,b],\ g$ is a differentiable function with non-zero continuous derivative on $[c,d]$ and the range of $g$ is contained in $[a,b]$, then $f\circ g$ is Riemann integrable on $[c,d]$.

Quote from Is the composite function integrable? See the last result mentioned in the paper.