Is it possible to upgrade a RAID5 array with 3 3TB HDDs to 3 6TB HDDs by swapping out the drives one at a time, letting each on rebuild, and then expanding the array to use the new space? I am currently using the Intel controller that is on my motherboard (Asus Maximus VI Formula) and the controllers ID is PCI\VEN_8086&DEV_2822&CC_0104.
It is possible. You will need to rebuild after replacing each drive.
You can use Windows* Disk Management to increase the volume size as explained in the Help section of Intel® Rapid Storage Technology; go to search and look for “Increasing Volume Size”.
Remember to back up your data before doing any change to the array.