Sorry about that! I read integra as integrated, hence why I went off on that route!
An integrated amplifier has two main parts:
A pre amp section - which is where you control which source you want playing, what level you want it to output (volume). These are what all the knobs do on the front of most hi fi amps.
And a Power Amp section - this is where the actual amplification is done, think of it as the muscle of the system.
Your Integra 30.3 is no exception:
The pre amp section allows you to select which source you listen to and control the volume. It also does the decoding etc.
The power amp section then beefs up the sound and sends it to the speakers. In your case 5 of them.
If you add a power amp for a certain channel (eg fronts) then you are using the pre amp in the Integra, but the external power amp for that channel. The two front speakers are then wired up from the power amp. Thus the speaker terminals on the back of your Integra for the front speakers are no longer connected to anything. To go back to your original scenario, the 100watts in your integra for the front channels are now redundant, and the 75watts that the power amp has is in use instead. Your rear and centre speakers are still connected to the Integra though and using its 100wpc power for their channels.
Another way to look at it is that you connect the power amp to the "Pre Out" sockets on the back of your Integra. These basically mean "Pre Amp output". What would normally be sent to your internal power amplifier is also being sent to your external power amp
I think your best solution to try and improve music playback would be to add a 2 channel stereo power amplifier, to power the fronts. This will definitely be the simplest too.
Dont get a 5 channel power amp, you simply don't need one. The other 3 channels it gives you are unnecessary, as your integra is more than capable of powering these. Also, these 3 channels (centre and rears) are not used when playing stereo music, so won't help you there. 5 channel amps are usually the domain of high end systems, where serious power is needed all round, and thus are expensive.
If you don't mind buying second hand from eBay, my advice would be to try and get hold of a decent 10ish yr old 2 channel power amp from there and give it a go. If you feel it does nothing for your set up, or you don't like the new sound, you'll almost certainly be able to resell it for what you paid (check previous sales first to get an idea of avg selling price).
I only ever recommend stuff I've heard, and so would advise to try something like the Arcam Alpha 8p, 9p or 10p, depending on budget (looking around £100, £175 and £250 respectively). If you dont mind going older, there are always plenty of Audiolab 8000p available around the £200-250 mark.
Finally, yes you can always bi-wire your speakers from any amp. If the amp has two sets of speaker outputs then you use one pair to the treble and the other pair to the bass. If your amp has only one set of speaker outputs, you simply take both treble and bass feeds out of the one set (so 2 wires into each connector). If you buy this cable new from your local dealer he will be able to put the right connections on it for you. Most important thing to remember when bi-wiring is to remove the metal link plates that join the two sets of terminals on the back of the speaker (as you are now feeding each on independently). You will create a short circuit if you don't. Google bi-wiring and you should see plenty of diagrams regarding all the above.