Be nice guys, they are obviously new to this stuff LOL
The answer is: "No, you can't run a sub off the integrated amplifier in your JVC head unit."
A subwoofer needs to amplify lower frequencies. The lower the frequencies you need to amplify, the more power you need to do it.
As an example, a typical tweeter may only be using 10-20 watts of power to play high frequencies at high volumes, but a 10" subwoofer would need hundreds (or maybe even thousands) of watts to play the lower frequencies at high enough volume to be balanced with the tweeter volume, which is only using 10 - 20 watts.