This question is driving me crazy. If you could explain it step by step, I would really appreciate it. Thanks in advance!

Question

Find y = f(x) if f"(x) = x+2, f'(0)=3, f(0)=-1

Answer 1

y'' = x+2

y' = (1/2)X^2 + 2x + C = f'(x)

f'(0)=3 --> C=3 ---> y' = f'(x) = (1/2)X^2 + 2x + 3

y = f(x) = (1/6)x^3 + x^2 + 3x + k

f(0) = -1 --> k=-1

y = f(x) = (1/6)x^3 + x^2 + 3x - 1