Bounded Function being absolutely integrable but not integrable

[jdz86]

Homework Statement

If f:[a,b] \rightarrow \Re is bounded then so is |f|, where |f|(x) = |f(x)|. Call f absolutely integrable if |f| is integrable on [a,b]. Give an example of a bounded function which is absolutely integrable but not integrable.

Homework Equations

None

The Attempt at a Solution

I was thinking \sqrt{x} but was unsure of how to show it.

 

[Dick]

How about looking for a nonintegrable function that takes only the values +1 and -1?