Answer
$y=\frac{1}{2}x^2-x-\frac{1}{2}$
Work Step by Step
Step 1. Given $\frac{dy}{dx}=x-1$, we have $y=\int(x-1)dx=\frac{1}{2}x^2-x+C$ where $C$ is a constant.
Step 2. Using the point on the curve, $y(-1)=1$, we have $\frac{1}{2}(-1)^2-(-1)+C=1$ and $C=-\frac{1}{2}$.
Step 3. Thus the answer is $y=\frac{1}{2}x^2-x-\frac{1}{2}$
