I'm a little unclear about what you're asking. By bounds do you mean region? Are you doing a double integral over some rectangular region and want to convert to polars? If so, the general procedure is to look at the boundary curves for the region and write each one in polars. The limits of integration are determined by the intersection points of the boundary curves.

The example you've given looks incomplete. However, the line with is in polars and the circle is

. Limits can't be determined until you specify the rest of the boundary for the region.