Integration in \(\mathbb{R}^2\) (boundary depending on \(y\))

Represented is the set \(M:=\{(x,y)^\top\in \mathbb{R}^2\,: \, c\leqslant y \leqslant d,\; \underline{x}(y)\leqslant x \leqslant \bar{x}_u(y)\). with \(x_l=y_l=0\) and \(x_u=y_u=1\)

\(c=\)
\(d=\)
\(\underline{x}(y)=\)
\(\overline{x}(y)=\)