Area under voltage vs time discharge curve
It's not the area under the curve but the partially discharged (final) level of the voltage that is important thing. The area gives you volt-hours and not ampere hours.

A manufacturer uses a constant current load and whilever the battery is able to produce above a "certain" minimum terminal voltage the hours that count the amps will keep ticking.

This, however does not mean that it will suit a specific target design. Here is an example of a discharge curve for a lightweight PP3 9V battery: -



Note that they define the end voltage and this means "end of test" because to drag more enrgy from the battery is going to either make it unsafe, unusable in 90% of target applications and render it impossible to recharge (if it were a rechargeable type). You have to set an end limit that is meaningful or you'd be conning the public.

Look at this AA battery: -



After just over 2 (and a bit) hours of 100mA discharge it's not a 1.5 volt battery any more. Another thing to watch out for is how they have used a constant current source - calculating ampere hour rating at 1mA gives you a better figure than at 100mA. Buyer beware and read the spec.

Take a look at the Duracell MN1500 battery and if you have any questions on this raise them. It should give you a good idea what a good supplier does to test their batteries.