Find the antiderivative of the function f (x) = 3x ^ 2-x whose graph passes through A (-3; 4)

Let’s find the antiderivative function according to the table of antiderivatives:
If f (x) = x ^ p, then the antiderivative will be F (x) = (x ^ (p + 1)) / (p + 1).
f (x) = 3x ^ 2-x.
F (x) = (3 * x ^ 3/3) – (x ^ 2/2) + C = x ^ 3 – x ^ 2/2 + C.
A (-3; 4).
(-3) ^ 3 – (-3) ^ 2/2 + C = 4;
-27 + 3 + C = 4;
-24 + C = 4;
C = 4 + 24 = 28.