Well you have that I=Integral(r^2*dm)
Then u have the density=Mass/Volume (I'm supposing it's a cylinder)
Then you solve I=Integral(r^2*density*dx*dy*dz) where r^2=x^2+y^2.
now you have the full cylinder without the holes.
Do the same for the holes and sum (with a minus of course)
Ohh if you're having trouble with the holes just integrate but using r as a vector. So you do r=x+(cos(tethta), sen(theta)) where x is the vector from the oringin to the center of the wholes. Using that r just repeat it for the 4 circles (it's simetrical). Just remember that when integrating area in polar coordiantes dA=dx*dy=r*dr*dTheta