Hello, 1. The problem statement, all variables and given/known data I was asked to prove that for f(x), Riemann integrable and bounded from above by real number M: ∫[a,b] f(x) < M(b-a) 2. Relevant equations 3. The attempt at a solution Since f(x) is Riemann integrable, ∫[a,b] f(x) must be equal to both the lower and upper Darboux sums. Therefore: ∫[a,b] f(x) = supf(x) [a,b]Ʃ[i=1,n]Δxi = supf(x) [a,b](b-a) <= M(b-a) I am really not sure this is rigorous enough, or even how it ought to be approached. I'd appreciate some guidance please.