Help with partitioning an interval for Riemann integral of piecewise function

If $$f(x)= \begin{cases} x &-1 then prove $$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.

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.

• but here the function is continuous. the page you refered me to is discussing of points of discontinuoity. Apr 22 '20 at 13:26
• Huh, I didn't even notice that it was continuous (I assumed the different pieces introduced a discontinuity). You should try to prove that every continuous function is integrable. Apr 22 '20 at 13:47
• Well that is what I had in mind. even choosing a function g on a broader interval to show f is differentable on all [-1,1]. but I believe I am supposed to use upper and lower sums. so there is no way to partition such interval? I ve been googling this for hours and I can not see any similar problem to see how this proof might look like. Apr 22 '20 at 13:51
• See here. Apr 22 '20 at 13:54
• the behaviour of function here is know on (-1,1], the question is asking wether it is integrable on [-1,1]. am I supposed to consider this at all? thanks Apr 22 '20 at 14:01