Let $\displaystyle f : [a,b] \rightarrow \mathbb{R}$ be increasing on the interval $\displaystyle [a,b]$ (that is, $\displaystyle f(x) \leq f(y)$ whenever $\displaystyle x < y$, so in other words monotone increasing). Prove $\displaystyle f$ is integrable on $\displaystyle [a,b]$.

By integrable, we're referring to Riemann integrable.

Any way, uhh help? Would I go about proving this saying that if we can prove its continuous, then its integrable? That's some theorem. But isn't it obvious it's continuous, as it says its increasing