this is an elementary question, but I don't know: What's the difference between active and in-active pick-up?
Actually it's active and passive. Active pickups use batteries and are widely considered more versatile and more easily controlled. Though sometimes passives are more suitable of course.
If you put a battery in the back, at least one of your pickups will probably be active
Warwick Jazzman
Hartke 1415 140Watt
Boss Overdrive
From what I've heard they're called active and passive basses. Active basses need a battery installed in the bass to run a preamp that's actually built into the bass. This preamp allows you to mess with your EQ without even going to your amp. Which makes changing tones simple, and allows for a more versatile sound.

A passive bass doesn't need a battery installed in the bass. These basses usually just have a volume and a tone control. Which would require you to go to your amp and mess with your amp settings if you wanted a different sound out of your bass.

It seems as though the pro's to an active bass are you can create more versatile tones and you have easy EQ access. The cons appear to be you have to pay for batteries and more wires could come lose, more stuff could break, etc.

But please correct me if I'm wrong because I don't know much about the subject.
There are two types of active on a bass

there are Active Pickups wich have a snappyer sound and more lows and clearer highs than a passive and gennerally a more "big/huge" sound.

then there is active EQ wich is have Bass and trebble boosters on youre bass ( a knob for bass and a knob for trubble) wich can boost and cut dbs of bass and trebble frequencies. and most upper end basses also have a midrange boost/cut.

you can have active pickups without active EQ or you can have passive pickups with a active EQ or Bolth active pickups and active EQ.

Active pickups use less windings and generally dont pick up any outside noise. what the pickup does pickup (wich in good brands like EMG is just youre bass) is then boosted with a preamp powerd by a battery giveing it more output then a passive pickups.

Advantages of Active pickup: more output, unique snappyer "crisp" sound that is very clean and pushes distortion harder.

Advantages of Passive pickup: more "classic" sound that is a bit nasely.

Advantages of Active EQ: more versatility. can get multiple different sounds. more control. and can make minor needed adjustments on youre bass in the middle of a song or between songs when you are live/playing in band setting and cant run to youre amp.
ESP B-405,Fender American Jazz Bass(EMG J active pups and LEO QUAN BADASS II ) squire P bass(EMG P active Pups)),
SansAmp Bass driver DI
Ampeg SvP PRO Tube Preamp
QSC2450 Power amp
Furman PL8