Determine the antiderivative of $f(x)=2x^2-x+15$.

This is a polynomial so we can use Antiderivative Rule 5 to find its antiderivative. Applying the rule we see that
$$F(x)=\frac{2}{3}x^3-\frac{1}{2}x^2+15x+C$$
where $C$ is the constant of integration.