1. The problem statement, all variables and given/known data Suppose g is a differentiable on [a,b] and f = g', then does there exist a function f which is not integrable? 2. Relevant equations 3. The attempt at a solution I've tried to look at pathological functions such as irrational, rational piecewise functions. but the g would not be differentiable. Moreover, it seems intuitive that the derivative of a function is integrable. Please help.