Let I = [ a , b ] {\displaystyle {}I=[a,b]} be a compact interval and let f , g : I → R {\displaystyle {}f,g\colon I\rightarrow \mathbb {R} } be two Riemann-integrable functions. Prove that f g {\displaystyle {}fg} is also Riemann-integrable.
![{\displaystyle {}I=[a,b]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d9415455379ef65b8bcc5629a5e182b7e8909e52)
