Answer
$$f\left( x \right) = {x^3} - x + 10$$
Work Step by Step
$$\eqalign{
& f'\left( x \right) = 3{x^2} - 1,{\text{ }}f\left( 0 \right) = 10 \cr
& f\left( x \right) = \int {f'\left( x \right)} dx \cr
& f\left( x \right) = \int {\left( {3{x^2} - 1} \right)} dx \cr
& {\text{find the antiderivative by the power rule}} \cr
& f\left( x \right) = 3\left( {\frac{{{x^3}}}{3}} \right) - x + C \cr
& f\left( x \right) = {x^3} - x + C \cr
& {\text{with }}f\left( 0 \right) = 10 \cr
& 10 = {\left( 0 \right)^3} - \left( 0 \right) + C \cr
& 10 = C \cr
& then{\text{ }} \cr
& f\left( x \right) = {x^3} - x + 10 \cr} $$
