Suppose I R is a closed interval and that f : [a; b] Ã I R is such that exists on [a, b] Ã I,

Suppose I Š‚ R is a closed interval and that f : [a; b] × I †’ R is such that exists on [a, b] × I, and for each t ˆˆ [a, b] the function x †’ f(t, x) is in R*(I) and there exist a, ω ˆˆ R*(I) such that the partial derivative satisfies If
F(t) := ˆ«I f(t, x)dx, show that F is differentiable on [a, b] and that

oflar (x) aft, x)/at o(x) for x E 1. ae. -