The marginal cost of a certain commodity is C'(x)= 3x^2 -36x + 120

Question

If it costs 5 dollars to produce 1 unit, then find the total cost of producing x units is...

Please how do I find the total cost?

Answer 1

if C'(x) = 3x^2 - 36x + 120
then
C(x) = x^3 - 18x^2 + 120x + c , (I integrated)
if x=1 then C(1) = 5
5 = 1 - 18 + 120 + c
c = -98

C(x) = x^3 - 18x^2 + 120x - 98