If you aren't pounding the snot out of it, the integrated amp should be fine and if you are pounding it, it should still be fine unless the sensitivity of those speakers is less than 86dB/1W.
The photo shows the specs for the integrated amp I'm using and it sounds great, has always sounded great and it has no problem providing more output than I need. The low end is rock solid and I would say it has always sounded very neutral, noise floor is very low and it was made in the '80s. If yours can do 2dB of dynamic headroom (same as mine), I don't think you'll have any problems. If you find that the volume control indicator tends to be near/at/above 12:00, you're nowhere near 75dB.