consider the function f(x) whose second derivative is f''(x) = 3x+2sin(x)

if f(0)=4, f'(x)=4. what is f(2) = ?

heres what i did

$\displaystyle f'(x) = \int (3x+2sin(x) $

$\displaystyle = \frac{3x^2}{2} - 2cos(x) + C1 $

$\displaystyle f(x) = \int \frac{3x^2}{2} - 2cos(x) + C1 $

$\displaystyle = \frac{x^3}{2} + C2 - 2sin(x) + C2 $