If \int_a^b f(x)dx=5 and \int_a^b g(x)dx=-1, which of the following must be true?

I. f(x)>g(x) for a\leq x\leq b
II. \int_a^b (f(x)+g(x))dx=4
III. \int_a^b (f(x)g(x))dx=-5

(A) I only
(B) II only
(C) III only
(D) I, II, and III