Answer
$y=10x-\dfrac{x^2}{2}-1$
Work Step by Step
We need to find the anti-derivative for $\dfrac{dy}{dx}=10-x$
Thus, we have $y=10x-\dfrac{x^2}{2}+C$
Apply the initial conditions in the above equation to solve for $C$.
we get: $0+C=-1 \implies C=-1$
Hence,$y=10x-\dfrac{x^2}{2}-1$
