@Dr.Fiero is correct, that's the test to do, but it can sometimes be awkward depending on setup. Capacitors can pass a simple DVM test, which is the second test you should do on them (the first is the visual examination as some show signs of failure). But the common DVM test is not under load. Damage to a cap is often proportional to its ability to hold a charge. (But all cap eventually fail, either gracefully or catastrophically). They make expensive testers (like car battery load testers) for capacitors; but unless you can match the test environment to your particular motor they aren't perfect either.
@Dr.Fiero 's suggestion, if you can do it, is a good one.
Contrary to popular belief its job isn't to store a charge and use it to "boost" power to start the motor. Single phase motors don't produce differential flux in their windings to start the motor like three phase ones do. The capacitor does this in the starter winding and kinda trick the motor into starting. When it fails, that means it leaks faster, so fast the flux isn't generated sufficiently to offset the primary winding, thus there is no counteractive magnetic field to start the motor spinning. Without a load the cap may pass the simple DVM test, meaning it DOES hold a charge, but that won't say if it has ENOUGH of a charge to get it started.
BTW what is the HP of the motor? I'll have to check but I used to have a brand new one around somewhere. Is yours belt driven from underneath?