Integrated amps with room correction...

The best unit currently is the Trinnov Amethyst. $11,000 with it's microphone. The microphone is sold separately as Trinnov figures most people will have the set up done by the dealer. No guts not glory. It does have a very nice computer interface. Its bass management is better than most but not as sophisticated as the Tact.  

The only way to do effective room correction is with a calibrated mic. You can not guess what the room and speaker are going to do (too many variables) you have to measure it. What are you going to measure it with? A thermometer? 
yyz illustrates the problem Tact had. The designer Radomir Bozovic aka Boz is the Russian PhD and the father of room correction could not understand how everyone could not think like he could and assumed his system was obvious and self explanatory. It was very expensive stuff so he decided to sell it directly to keep prices down. His instruction manual sucked and the little company got buried in phone calls and very unhappy customers who could not make things work.  You had to sit down with the computer and trundle though things until you got yourself on the learning curve. Then the sailing was pretty smooth. If you ran into a brick wall you called Tact and spoke only to Boz. People want plug and play and the Tact units were anything but. But, if you put in the time and learned how altering target curves and delays would affect the sound you could make your system do amazing things. They were a tweaker's paradise. 
Anyway the company went under and Boz disappeared. My guess is that he owed investors a lot of money. Lyngdorf was a partner initially. You can still see some of Boz's design in the Lyngdorf units. They are easier to use but not as near as sophisticated and flexible. My Tact 2.2X is still going strong and there is nothing on the market yet that I wish to trade it for the Trinnov is close but the bass management is not near as good as the Tact's. I can change high and low pass filters independently one Hz at a time on the fly from the listening position from 20 to 300 Hz, 1st to 10th order!  How can you beat that? 

Mijoystyn, Trinov's piece is $10k and is a preamp/dac with room correction, it is not what the OP was inquiring about.

Room correction can be awesome the Anthem STR preamp is quite fantastic and a bargain at its price compared to the Amytheist.

Most people are not looking for the end all and be all in room correction just to correct some of the room's gross errors, almost all commercial room correction systems can do that. 

It will then come down to how easy the unit is to use as well as the sound quality of the unit's dac and preampliifer stage.

If you look at all the rave reviews of the Micromega M150 you will see why we endorse it, and its room correction system does work and it comes with a calibrated microphone.

Dave and Troy
Audio Doctor NJ Micromega and Anthem dealers

I own a Lyngdorf TDAI 3400 and I'm very happy with it. Room correction is real and obvious. Few of us have perfect rooms and/or the expertise to correct with various sound treatment articles. The Lyngdorf replaced a Mark Levinson 326S pre and 532H amp, btw.

The upcoming Arcam SA30 has Dirac.