Chapter 4: Applications of Derivatives - Section 4.7 - Antiderivatives - Exercises 4.7 - Page 240: 72

$y=10x-\dfrac{x^2}{2}-1$

The anti-derivative for $\dfrac{dy}{dx}=10-x$ is $y=10x-\dfrac{x^2}{2}+C$ Now, apply the initial conditions in $y=10x-\dfrac{x^2}{2}+C$ to get the value of$C$. This implies $0+C=-1$ and $ C=-1$ Hence,$y=10x-\dfrac{x^2}{2}-1$