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## Homework Statement

Suppose f(x):[a,b][tex]\rightarrow[/tex][tex]\Re[/tex] is bounded, non-negative and f(x)=0. Prove that [tex]\int^{b}_{a}[/tex]f=0.

## Homework Equations

## The Attempt at a Solution

I am trying to use the idea that lower sums are zero, and show that the upper sums go to zero as the norm of the partition goes to zero. That is Upper sums [tex]\leq[/tex] c||P|| such that [tex]\int^{\overline{b}}_{a}[/tex]f=0.

how can I prove that statement by using the idea above with the choice of c?