I'm not much of a graphics guru, so maybe someone else will have a
better suggestion, but until then...

   If you know how that the background is white, for example, and you want
to fill the exterior with blue, then paint a blue rectangle, then paint a
white arc over the blue rectangle.

   If you don't know that the background is white, you could try using
tricks with masks so as to paint the rectangle, then "unpaint" the region
under the arc.

   If you have anti-aliasing turned off, you could try painting the
rectangle, and then the arc on an offsurface buffer, and then copy and paint
the image of that buffer onto your target buffer with parts of the image
being transparent.

   If you want to go with fillPoly, you could either use a straight-edge
poly and approximate the arc with lots of points (search math sites to find
the formula for arcs). Otherwise, you might be better off using nurbs.

   - Oliver

If you're using any remotely modern Java platform, then you can cast the
Graphics object to Graphics2D, and do this fairly easily:

   import java.awt.geom.*;

   ...

   Graphics2D g = (Graphics2D) ...;
   Rectangle2D rect = ...;
   Arc2D arc = ...;

   Area a = new Area(rect);
   a.subtract(new Area(arc);

   g.fill(a);