I have recently been trying some questions on improper integral and I saw this written over somewhere.
$f$ is a continuous function from [$0,1$] to $\Bbb{R}$ and $f$(t) $\geq$ $0$
We define $g$(x) = $\int_{0}^x f(t)dt$
Then m $\le$ $g$(x) $\le$ M?
where M is $\sup_{f}$[$0,1$] and m is $\inf_{f}$[$0,1$]
Is this true?
The question actually was to show that $g$ is bounded.I think I can prove that value of $g$ lies between $0$ and M.But I am unable to show that it lies between m and M.
Help,please