Replaced answer...
For no reason would a car mysteriously die and shut off at a snap of a finger from a "going dead battery" and alternator.
Good to check those but check your main relay's grounding/power source.
it could be the main assembly relay under the drivers kickpanel
what model is ur integra? it could be a integra ls tranny or u have a integra gsr that comes with a gsr tranny
it is possibly your calipers and or rotors.
could not be getting spark our gas our timing belt no good
could it be the thermostat or the fan itself?
The top control arm bushings are likely candidates.
lug nut were loose
Water pump, Radiator, thermostat, low coolant, blown head gasket, busted hose. Could be one or all but I would check these first.
could be a bad fuel pump or fuel filter. have a friend crank the car as you bang on the fuel tank.this can some times free up the trash on your fuel pump.
There is a problem with power to that part of the vehicle. Check fuses as well as all wiring. Make sure that the ignition switch is operating properly and turning power on to these areas.
check the fuel lines.. fuel relay, fuses, and if all else fails the pump.
problem could be the rear strut