HP42s first major program (Double Integral) Best way to approach?

[Werner]

This one, not Albert's last one:

\(I = \int _0^c \sqrt{c^2-x^2}\left( \sqrt{b^2-x^2} - \sqrt{a^2-x^2} \right)\;dx\)

Which I posted before, but not in pretty print; figured out how to do that in the meantime.
This is the integral solved by the BORE program;
Werner