JEE Math Practice Question

Let a function ƒ : [0, 5] $$ \to $$ R be continuous, ƒ(1) = 3 and F be defined as : $$F(x) = \int\limits_1^x {{t^2}g(t)dt} $$ , where $$g(t) = \int\limits_1^t {f(u)du} $$ Then for the function F, the point x = 1 is :

1. A.a point of inflection.
2. B.a point of local maxima.
3. C.a point of local minima.
4. D.not a critical point.