It's not low enough to rule out inaccurate voltmeter...

It's also not low enough to cause this problem.

Check whether the distributor gets power (like it should) when the key is at 'RUN'. Then check it again while cranking. Flaky switch isn't real unusual for Honda overall, but I don't know specifically for Integra. If you can make it stall by wiggling the key, or by holding the key slightly off-position, that also points to the switch.