Riemann-integrable/Nonnegative/Continuous in a point with positive value/Positive integral/Exercise

Let $f$ be a Riemann-integrable function on $[a,b]$ with

$f(x)\ge 0$

for all $x\in [a,b]$. Show that if $f$ is continuous at a point $c\in [a,b]$ with $f(c)>0$, then

${\int }_a^{b}f(x)dx>0.$

Create a solution