Actually Microsoft could not legally integrate the Linux kernel and Windows because of the license that Linux is released under. The GPL forbids outsiders from closing the source. Only a joint effort by every single person that contributes to a project released under the GPL can result in a relicensing of the code. To add more fuel to the fire, that relicensing isn't retroactive. All previous releases are still GPL'd therefore Microsoft would have to get a list of every single last person that put code into the official kernel distribution's core and bribe them to relicense. What they would end up getting at the most would be maybe bits and pieces of the kernel.
If Microsoft were to put any linux kernel code in Windows the entire Windows product would have to be released under the terms of the GPL. That is a requirement of the GPL, if you use any code from a product released under the GPL then you have to release your product under the GPL. The GPL simply put doesn't tolerate freeloaders. So RedHat, et al would go after Microsoft for a contract violation on behalf of the FSF, not anti-trust violation. It could also result in a criminal indictment of Microsoft officials for copyright infringement.