You can do this if you don't want to spend any money (very little, though . . ) for the cables etc. recommended here.
If the mobo has the USB3 plug on it, with the motherboard you will also get a PCI backplate with two USB ports at that end, and the motherboard plug on the other.
Unscrew the plate from the plugs. connect the other end of the cable to the motherboard. Plug in your case's USB3 ports to one of the plugs, and tape it with automotive self-adhesive rubber hose bandage. (Or just use electrical tape).
You would then have one of the plugs remaining to be used. For about $25, you could then get one of these or something similar that would fit a 3.5" drive bay or a 5.25" bay with the adapter:
http://www.newegg.com/Product/Produc...82E16817801091
On this particular item at the Egg, two customers isn't even a sample by small-sample methods. I got the SYBA, and haven't had trouble with it (used as I described.)
But with that, you lost two USB 3 ports by the disassembly I described, and gained four -- in addition to the ports build in to your case.