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

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

${}f(x)\geq 0\,$

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