Let f : [a, b] -> R be a positive continuous function, i.e., f(x) >= 0 for all x in [a, b].

I want to show that the function F : [a, b] -> R defined as F(x) = integral of f with limits x and a, for x in [a, b] is monotone increasing (i.e., F(x) >= F(y) if x >= y).

any ideas? thankz