1. The problem statement, all variables and given/known data Let f map [a,b]-->R be a continuous nonegative function. Suppose Integral f(x)dx from a to b = 0 show that f = 0 on [a,b] 3. The attempt at a solution Just not sure if this is good or not.. so the lower sum <= 0 = integral f(x) dx but the lower sum must be 0 since f is non negative. now if f >0 then the lower sum >0 so this is a contradiction, f = 0.