Solve the differential equation

Question

f"(x)=x^2, f'(0)=3, f(0)=-1

Answer 1

f" = x^2
f' = 1/3 x^3 + c
f'(0)=3, so c=3 and
f' = 1/3 x^3 + 3

Now do that again going from f' to f.