Please someone help me with my last question on antiderivatives, PLEASE!

Question

Find the particular antiderivative of the following derivative that satisfies the given condition.

C'(x)=6x^2−4x​; C(0)=1000

    

Answer 1

C(x) = 6x³/3 - 4x²/2 + k

C(x) = 2x³ - 2x² + k

C(0) = 1000 ⇒ k = 1000

C(x) = 2x³ - 2x² + 1000

Test the answer.