1. The problem statement, all variables and given/known data The original question required me to show that for f(x) >= 0 for all x, f continuous, where the integral (from a to b) of f =0, that f(x) = 0 for all x in [a,b]. I did that, using a proof by contradiction. Second part of the question requires me to show that the two hypotheses (f(x) being >= 0 and f being continuous) were required. 2. Relevant equations 3. The attempt at a solution I think counterexamples would show this, but can't figure out what would make a counterexample. Do I need to take f(x)<0 for f continuous and show that its integral can't equal zero? Similarly, take f(x)>=0 but not continuous and show that its integral also can't equal zero?