There actually are systems out there that do bolt-up toward the rear of the car in place of the mufflers. I've never seen anything for Integras, as most of them are for domestics.
The company name is STS - Squires Turbo Systems
This is their Z06 bolt-on system.
Here are some of the benefits listed on their website:
-Ease of installation
-Less noise and heat in the passenger compartment
-No need for expensive headers, mufflers, or exhaust systems
-Approximately 500F lower turbo temperatures
-Lower underhood temperatures
-More room under the hood
The last four are biggies
But with all of this piping one has to ponder the amount of turbo lag it would produce.
Think about crusing at a relatively low speed, then suddenly jumping on it. It would take the increased exhaust pressure forever to get to the turbines, and then it would take another forever for the compressed air to get back up to the throttle body. I don't know though, maybe the lag isn't as pronounced on big-displacement domestic V8s. But they do offer systems for V6s like Cadillac's CTS.
And what happens when you hit a puddle and water splashes all over the snails?
As I keep saying..turbos make good mufflers! I don't know why nobody believes me. They really do muffle engine noise.
Anyways OP, this company does make universal systems, but you're a lot better off just going with a conventional set-up. It's proven, it works, and there is a lot of parts and support available.