= Solution
The <integration region> lies between the line $y=x$ and the <parabola> $y=x^2$, with $-1\le x\le0$. 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>.
\Image[/past-exam-of-the-mathematical-methods-ii-course-of-the-university-of-oxford/2016-resit-integration-regions.png]
{title=Horizontal slicing and two changes of variables for the integration regions}
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