If f'(x) =3x 2 -4x +5 and f(1) = 3 then find f (x) .

Answer 1

f'(x) = 3x^2 -4x + 5 (integral of ax^b = (a/(b+1)x^(b+1))

f(x) = x^3 -2x^2 +5x + c, plug in x=1 to solve for c

f(1) = 3 = 1-2+5+c

c =-1

f(x) = x^3 -2x^2 + 5x -1