For $f(x) = \begin{cases} 1, & 0\le x\le1 \\ 2, & 1<x\le2 \end{cases}$
Use the definition of the Riemann Integral to show that $f$ is Riemann Integrable over $[0,2]$.
It was suggested that I use the partition $(0, 1-\epsilon, 1+ \epsilon, 2)$ and let $ \epsilon\rightarrow 0$. Unfortunately, I am unsure how to do this. Any guidance would help.