No, they're not trouble prone. Just change the ATF every 30k or 2 years and you're good to go. Very easy to work on, you just pull the plug behind the passenger side front wheel and drain out ~2.5 quarts and refill through the dipstick tube.
AFAIK the only troublesome Honda ATs are the 5-speed autos from a few years ago. That Integra should have a 4-speed, which is fine. [/quote]
I have an 01' Accord 4 cylinder w/ 4 speed BAXA A/T and it is one of Hondas failure-prone units. They extended the warranty to 91 months and 109K (because of a class action suit, I think). Certain year Civics and Odysseys also had trouble-prone A/T's.
The problems with Honda A/T's are more wide spread than people realize.