Adding Subwoofer and Amp to Integrated Radio

[bakerman6578]

ALRIGHT, so this is my first post here I think, or at least in a long time, Well long story short I had a 66 Mustang as my daily for the last 3 years... and well going to college this is no longer gunna work... so my dad bout a new Aspen, and I am going to use the Yaris as my Daily transportation now. Now it is an 2007 Sedan with the integrated radio and this thing has very little bass and distorts very easy at higher volumes so here's my plan before I completely melt the stock speakers. In the Mustang I have 2 Kicker 400.4 amps and a 2000 watt mono block JVC. I love sound and besides going fast its my other passion. Unlike my dad the stock audio system only cut it for me for a week or 2 and im ready to upadate some now.
Im thinking im going to take one of the Kicker 400.4 out of the mustang (it was overkill anyway) and use it in the Yaris. Now the amp is capeable of High Level input so what I am thinking about doing to start with it using the wires from the back speakers as the inputs to the amp. Wire 2 channels to a new set of 6 by 9s and bridge the other 2 channels into some sort of subwoofer setup. I know the 6 by 9's will work but my concern is the subwoofer because I really dont want to change the headunit. I think the single DIN's look cheesy in these cars and dont wana drop a grand on a decent Double DIN. So keeping the stock head unit... will it output frequency's low enough to make the subwoofer run halfway decent?
I know I am not going to get spectacular sound with a stock head unit, but I think I can make a drastic improvement over stock with some tweaking and tuning. Thank YOu for advice in advance. I have been reading on here ALOT over the last couple weeks and learning that that Yaris isn't as bad of car as I had precieved.