4. (10%) (a) State without proof the Fundamental Theorem of Calculus. (b) Let F be a differentiable function on (-oo, co) such that F(-1) = 2, F(0) =1, F(1) =, F(2) = F(3) = 3. Evaluate, if exists, the following limits: i. lim F(x) dx - F(x) dx ). t-2 t - 2 Jo Jo 2n ii. lim - where f(x) = F'(x) is the derivative of F. n-too n n r=n+1 [Show your calculation.]