Let $f,g$ be bounded real valued function defined on $[a,b] \subset \mathbb{R}$. My source says that:
Suppose that $f(x)< g(x)$ for all $x\in [a,b]$ and $f,g$ are Riemann Integrable on $[a,b]$.
Then $\int_a^b f \leq \int_a^b g$.
I do not understand why $\le$ is used instead of $<$.
Is this meant to imply that the equality case exists? If so, could you provide an example?
Thanks for your help.