Help with partitioning an interval for Riemann integral of piecewise function

Question

If $f(x)= \begin{cases} x &-1<x\le0 \\ x^2 &0<x\le1\\ \end{cases} $ then prove $f$ is integrable on $[-1,1]$

I am studying this topic, and my textbook has no example how to partition a piecewise function. I know the formulas for lower sums and upper sums, but I need some help with partitioning and deciding for component intervals, please.

Answer 1

You can use this result to easily prove your proposition. It is worth thinking about this construction in general, but also how it would be specifically applied to you problem.