What you really seach for is the mean of y.
The definition of the mean is
In your case
You must do the top part using part integration.
Find a number h such that y=h would cut the region into two equal areas.
Now, I found out that the center of mass is (1,3.6), but how do I find the line? Do I just find the line that cut across (0,0) and (1,3.6)? The problem is the hint says that I need to integrate the area with respect to y, but I don't know how that is going to help.
I used to do these problems by simply finding the bounds of the area of integration - in this case you need to know the y min and max values of the region. Then you just say , where a and b are your min and max.
This is essentially the same thing that CB suggested, but to me it is easier this way.