REW is a powerful measurement/analyzation tool, and it can also generate EQ filters based on its measurements that you can then use in various apps and devices. REW has many uses beyond generating EQ settings and measuring, but that's the part we are talking about, so...
You can use REW to measure your room response, and then either use its auto-generated EQ filters, or create your own. You put these filters into the miniDSP or whatever your EQ tool is. Then you measure again with REW to confirm how well the EQ works, and then you tweak your EQ some more, and you repeat that process until you are happy. There are several guides on how to do this. You do not need Dirac to do REW and EQ, but you can layer Dirac on top if you want (I did this and got the identical Dirac result as not using any of my own EQ, and found my own EQ efforts to be a waste of time).
Dirac is a mostly automated room correction software that walks you thru room measurements and then does an automated correction with more than just EQ. It does not integrate with REW, but you can use REW to measure before and after and see how it did, and also maybe make further tweaks in Dirac using REW to confirm if you want. You do not need to do any EQ filters on your own with Dirac, but you can.
In my opinion, EQing on my own took WAY more time and knowledge than Dirac, and I was not able to get nearly as good of a result on my own as I was with Dirac. I think the $200 is totally worth it, but your mileage may vary.