A function has a derivative of $f^\prime(x) = 6x^2 + 12x-7$.

1. If $f(0) = 0$, what was the original function?

   Step 1(a):

   Step 2(a):

   Solve for C by evaluating $f(x)$ at $f(0) = 0$.

   Hint (a):

   Note: you could also use the expression

2. If $f(-2) = 25$, what was the original function?

   Hint 1(b):

   $f(x) = 2x^³ + 6x^² − 7x + C$
   Evaluate the given point to solve for $C$.

   Hint 2(b):

   Note: you could also use the expression

3. Describe how you found the constant of integration in parts (a) and (b).

   Hint (c):

   Refer to hints in part (a) and (b).