1. The problem statement, all variables and given/known data Let f:[a,b] -> R R being the set of real numbers If f^3 is Reimann-integrable, does that imply that f is? 2. Relevant equations If f is Riemann-Integrable, then it has upper/lower step functions, such that the difference between the upper and lower sums is less than any [positive] epsilon. 3. The attempt at a solution I'm having a difficult time figuring out what it looks like for f^3 to be Riemann-integrable or, even f^2, for that matter.