How to calculate this area in $\mathbb{R}^2$? Write the area $D$ as the union of regions. Then, calculate $$\int\int_Rxy\textrm{d}A.$$
First of all I do not get a lot of parameters because they are not defined explicitly (like what is $A$? what is $R$?).
Here is what I did for the first question:
The area $D$ can be written as:
$$D=A_1\cup A_2\cup A_3\cup A_4\cup A_5.$$
Where: 
$$A_1=\{(x, y)\in\mathbb{R}^2: x\geq-1\}.$$
$$A_2=\{(x, y)\in\mathbb{R}^2: y\geq-1\}.$$
$$A_3=\{(x, y)\in\mathbb{R}^2: x\leq1\}.$$
$$A_4=\{(x, y)\in\mathbb{R}^2: x\leq y^2\}.$$
$$A_5=\{(x, y)\in\mathbb{R}^2: y\leq1+x^2\}.$$
First, for me I see that $D$ is the intersection of these regions and not the union. Am I wrong?

P.S. This is a homework.

Hint: the area inside each of the parabolic indentations is
$$
\int_{-1}^1(1-x^2)\,\mathrm{d}x
$$
