Integration methods...an error-proof method?

[AlexFekken]

I would say: do the math. Analyse any "bad behaviour" and either factor (transform) it out or use an algorithm that is suited to the particular type of issue(s) (thinking of Gauss-Legendre with weight functions for example). Of course chopping up the interval of integration to isolate the issues as much as you can first is probably a good idea as well.

But perhaps I am just too old to expect any silver bullets...