I didn't see a reply to my last message, so I'll repost it in case it got over looked. If someone replied, can you please repost it because I didn't see it.
Something was really weird with MultiSim, maybe I had too many programs open the night I typed this question causing it to slow my PC down. After the op-amp went to the rail, there was a delay before the RC started rising. That really threw my understanding of an intergrater circuit off.
I tend to get baffled by the "outside" of the circuit and not think about the simpliest thing "the inputs are 'equal'", that explaination you gave made perfect sense.
You never got to the question about putting a cap from the resistor/capacitor junction (the inverting input) to ground. I saw a circuit with this capacitor and wasn't sure how to "add" that into the equation. Per MultiSim, it only changed things VERY little. Keeping in mind I use an ideal op-amp (no offset voltage, bias current, etc..) so when I calculate something and run it in MultiSim, my answers should be just about identical.
The caps aren't in parallel or series because I tried both and my numbers were out in left field.