Definite Integrals please help

1.Let f(x)= 4x^3 + 3x^2 + x.
Find the value of x for which
F(x) = ∫(from x to 2 ) f(t) dt is the maximum,
and the maximum value of F(x).

2. Find the function f(x ) that satisfies the following condition.
f(x)= x^2 + ∫(from 0 to 1 ) x f(t) dt