First I want to refer to show that if $f:[c,d] \rightarrow \mathbb {R}$ is continuous and $g:[a,b] \rightarrow [c,d]$ is Riemann integrable, then $f\circ g$ is also integrable.
My case is slightly different with above link. Question: If $f:[c,d]\to\mathbb{R}$ is Riemann integrable and $g:[a,b]\to[c,d]$ is continuous, then is $f\circ g$ also integrable?
I guess that it's not true but I failed to find a counterexample. Please help me.
