first of all , when change to polar coordinates, you must know that there are "natural" limits of new (how u wrote) r and
but that only means that boundary can't go beyond the "natural" limits, but can go under...
if there is no "restriction" then they will be natural but if u have let's say some conditions then they probably will be changed
I prefer to use and but it's the same
most times your boundary will be shown with some region, like few lines, parabola, circle's or anything else, and now u put in that conditions your polar x,y, and solve ... to find how does your boundary change
in your example there is 2 boundary's , first is line x=y or y=x , and second y=6... so what that means it means that your integral will look like on the graph put the "new" x,y, in that equations and see what conditions will u get
can u do it ? and conclude something try and we'll see are you on the right track