 Solution

The integration region lies between the line $y=x$ and the parabola $y=x^2$, with $-1\le x\le 0$. It has a portion below the $x$-axis bounded above by $y=0$, and a portion above it bounded below by $y=0$. Horizontal slices change form at $y=0$; keeping that split is essential when reversing the order of integration.