Calculate center of mass multiple integrals Can you help me with this problem?

Find the center of mass of a lamina whose region R is given by the inequality:


and the density in the point (x,y) is :



The region r is this one:



Is this the proper way to set up the integral for m:

$$\int_{-1}^{1}\int_{-x-1}^{x+1} \ e^{x+y} \ dy \ dx$$

Any help?  Thanks
The integral for total mass is $$\int_{xmin}^{xmax}\int_{ymin}^{ymax} \delta(x,y) \ dy \ dx$$ where the range $(xmin,xmax)$ is the whole range of the shape and the range $(ymin,ymax)$ is the range in $y$ at a given $x$.  Can you put the correct limits on?  Can you do the integral?
Rotate the entire thingy by angle $\frac{\pi}{4}$. Integrations will be
$$\int_{-1/\sqrt{2}}^{+1/\sqrt{2}}dx\int_{-1/\sqrt{2}}^{+1/\sqrt{2}}dy \;\;\delta'(x,y)$$
etc. where
$$\delta'(x,y) = \delta\left(\frac{x+y}{\sqrt{2}}, \frac{-x+y}{\sqrt{2}}\right)=e^{y\sqrt{2}}$$