Uhhhh, the speakers are pioneer paper speakers so if they sound like **** you need to get new ones. I bought lightning audio from walmart but plan to go polk or some component speakers with an amp in the near future if you are looking to get a decent sound out of your car then you could buy the polks my friend has them in her maxima and they sound pretty good. Also you might want to upgrade the head unit. Also if you are looking to get a lot of base, then you can invest in a system but to me it adds a lot of weight I can do without.
If you do decide on putting new speakers in make sure the mounting depth is not too deep and dynomat never hurt any one.But if you put something like Polk speakers in your car like BlknBlTeg is saying you oem head unit is not going to have enough amps to push thoes speakers and will not sound the way they should. Then your looking at a new head unit that can support a 4 channel amp to drive something like that.
It sounds like you still have alot of reading to do. Stereo systems should be looked like performance parts for your integra, a system. The components need to be able to work together for the final sound you wish to acheive.