Elementary integrals of abs(x) fail. For instance:

integrate(abs(x),x=0..1,"noPole")

(7) "failed"

And in the sqrt(x^2) equivalent, they may be wrong. E.g.:

integrate(sqrt(x^2),x=-1..1,"noPole")

(13) 0

Some more examples here:

http://axiom-wiki.newsynthesis.org/SandBoxAxiom