A cubic polynomial function f is defined by f(x)= 4x^3 + ax^2 + bx + k

Where a, b, and k are constants. The function f has a local minimum at x = -1, and the graph of f has a point of inflection at x = -2.

A) Find a, and b.

B) If the integral of f(x)dx with bounds 0 to 1 is 32, what is the value of k?