Question about Intel graphics

I've got a few questions about Intel graphics. I'm sorry to be so disjointed and scatterbrained, but the whole situation seems quite convoluted, as far as I can tell.

I searched newegg.com for motherboards with integrated Intel graphics, and the compatible processors for those boards were all various combinations of Pentium, Celeron, and Core 2 Duo/Quad/Extreme. None of them seem to support the newer Core i# processors.

According to http://en.wikipedia.org/wiki/List_of_Intel_microprocessors#64-bit_processors:_Intel_64_.E2.80.93_Nehalem_microarchitecture, the newer Intel Core i3 includes an "Integrated HD GPU", as does the Core i5 Clarkdale, but not the Core i5 Lynnfield (whatever that means). According to that page, none of the Core i7's do.

So if I understand this correctly (and if I'm wrong, please enlighten me), the older Intel GMA graphics were built into the motherboard (like the GMA 950, or the GMA X4500). These are all fully compatible with free software (with the exception of the GMA 500). But the newer Core i# processors aren't compatible with those motherboards. Instead, some of these processors have integrated graphics capabilities built into the CPU itself, rather than the motherboard.

If that's all correct, then my question is: are the integrated GPUs that are built into the newer Core i3 and Core i5 processors compatible with free software? Is there any information on this? Has anyone tried running Trisquel or another fully free operating system on such a machine?