Let f be an integrable function on [a,b]. Suppose that f(x)≥0 for all x and there is at least one point $\displaystyle x_{0}$ ∈ [a,b] at which f is continuous and strictly positive. Show that

b

$\displaystyle \int$ f(x)dx>0

a

I think I am missing something because it looks too simple, since the function is continuous and strictly positive doesn't the integral have to be >0?