University Calculus: Early Transcendentals (3rd Edition)

We need to find the anti-derivative for $\dfrac{dy}{dx}=-x$ Thus, we have $y=-\dfrac{x^2}{2}+C$ Plug in $x=1,y=1$ into the above equation to solve for $C$. we get $C=\dfrac{3}{2}$ Thus, $y=-\dfrac{x^2}{2}+\dfrac{3}{2}$; which shows graph (b) with a concave-down parabola.