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## Homework Statement

Let f be positive and bounded over [a,b]. If f^2 is integrable over [a,b], then show that f is as well.

## The Attempt at a Solution

I'm just trying to use the fact that the upper and lower sums of f^2 over a partition P are arbitrarily close, and then somehow find an upper bound for the difference of the upper and lower sums of f based on that. I've tried separating it into cases, where the max and min of f on an interval are >=1, <1, etc. but it hasn't really led anywhere. If anyone could give me some sort of hint, i'd really appreciate it =)