If f'(x) = 3x^2 - 6x +3, find f(x) if f(0) = 2

Given that f'(x) = 3x^2 - 6x +
3

We need to find the function
f(x).

But we know that f(x) = Integral
f'(x).

==> f(x) = Int (3x^2 - 6x + 3)
dx

==> f(x) = Int (3x^2) dx - Int 6x dx + Int 3
dx

==> f(x) = 3x^3/3 - 6x^2/2 + 3x +
C

Let us simplify.

==>
f(x) = x^3 - 3x^2 + 3x + C

But we know that f(0) =
2

==> f(0) = 0 - 0 + 0 + C =
2

==> C =
2

==> f(x) = x^3 - 3x^2 +3x + 2