If f(x) ≤ g(x) on the interval [a,b], then the integral of f(x) is less than or equal to the integral of g(x) on the interval [a,b]. As a special case, if m ≤ f(x) ≤ M on [a,b], then the integral of f(x) is between m(b-a) and M(b-a). You can visualize all of this in terms of areas.