For anyone who finds this thread in the future looking for the same answer I was, here is what I did.
I made a complete backup of the data drive. (Actually I made 2 complete backups in case one of them failed.)
I then turned off the computer and physically removed 1 of the old drives. I replaced it with 1 of the new bare, unformatted drives. The new drive was identical to the old one. You do not need to format it.
I booted up the computer. The BIOS screen showed the array as "degraded". Once Windows came up, I opened Intel Rapid Storage. On the IRS screen there was a link that said "Rebuild to a new drive". I clicked that link and a new screen popped up saying to select the new drive to rebuild to. It showed the new drive I had just installed with a radio button next to it. I selected the radio button and then clicked a button at the bottom of the screen that said "Rebuild".
IRS then proceeded to rebuild they array. It showed the percentage of completion of the rebuild as it worked. My particular array consisted of four 2TB drives and was about 97% full. It took about 5 hours and 15 minutes to rebuild the array for one drive. While it was rebuilding, the screen showed a graphic that listed the 4 good drives and the 1 drive that was "missing" which was the old one I took out. Once the rebuild status reached 100% it then changed the array status to "Normal" and the missing old drive was removed from the graphic.
I then turned off the computer and repeated the process again with the next drive. I removed and rebuilt each drive one at a time until all 4 had been replaced. After performing this process 4 times I now have 4 brand new zero hour drives in a rebuilt array without losing any data. The total rebuild time was about 21 hours which is faster than I had guessed.
Hopefully this will help someone facing the same need to replace a failed drive or all their drives in an Intel Rapid Storage Raid 10 array.