Depends. In US you have one year warranty unless you get AppleCare. In Europe I believe everyone has 2 years. Battery is same as computer with time. Keep in mind, that if you would put on lots of cycles, time may not matter. battery is "consumable" and should last N cycles (specified for each model on Apple web site) with above 80% capacity.
If it is bulging, they might replace it for free, depends. It is safety hazard and they were replacing those for free. Someone may know if this specific computer is covered by some extended warranty deal... Best is to go to Apple and ask, they will tell you.