I took a short break from the rudin-crunching. I'm now doing reimann's integral. Anyhow here's a question I've having trouble with. Does f^2 is integrable imply that f is integrable? -No, take f=1 on rationals, f=-1 on irrationals on [0,1]. Does the integrability of f^3 imply that f is integrable? I can't find a counterexample. I'm not asking for a proof but a counterexample if there is one and if there isn't just let me know! thanks for any help.