If $f$ is integrable on a rectangle $R\subset \mathbb{R}^n$, prove that $f$ is integrable on any rectangle $R'\subset R$.
I tried to prove it in a similar way to prove that if $f$ is integrable on $[a,b]$ so it is on $[a,c]$ and on $[c,d]$ with $c\in[a,b]$. However, i didn't know how to use this fact. I would appreciate any suggestion :)