You do have a big problem. Try and see if you can figure out where oil is coming from, my guess would be transmission, obviously. It seems to me if something happened in there that was bad enough to make it leak is definitely not good. It is possible that the drain plug fell out or is not tight enough. Check your tranny oil/fluid, I am not familiar enough with the G-2 integra to tell you where exactly, but on passenger side below the drive axles is likely.