I am having a problem with the following exercise.
Let $f$, $g$ be continuous non-negative functions on $[a,b]$, and let $C$ a positive constant.
Suppose that: $f(x) \leq C+ \int_{a}^x f(t)g(t)dt$,
for all $x \in [a,b]. $ Show that:
$f(x) \leq C\exp\left(\int_{a}^x g(t)dt\right).$
Thank you in advance