For a differentiable function F, its derivative f satisfies f(x)>0 and f′(x)<0 for 1<x<5. Which statement best describes the behavior of F on the interval (1,5)?
a) F is decreasing and concave down on (1,5).
b) F is increasing and concave down on (1,5).
c) F is increasing and concave up on (1,5).
d) F is decreasing and concave up on (1,5).