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