Integration methods...an error-proof method?

[Matt Agajanian]

Hi all.

Although methods like Simpson's and Trapezoidal need evaluation at the endpoint, I can see a minefield if either endpoint produces a mathematical discontinuity or undefined result thus causing an HP-67, 41, etc. program to stop. So, it seems that error-checking or implementing an error-handling flag setting (HP-41, 42, etc.). Thus, further necessitating error-handling program code.

So, rather than this approach, what are some improved integration methods to avoid, aleviate, bypass, or resolve discontinuities in functions?

Thanks.