A busted capacitor can be obviously broken (leaking brownish fluid, corroded, or with the leads severed), but sometimes it's subtle. The top of a blown capacitor will be slightly bent outwards in a convex shape, rather than flat or slightly indented inwards like a working capacitor. See the photos above for examples.
Think of it like a vacuum-sealed glass bottle. When the seal is intact, the bottle cap is flat, and when you break the seal, the bottle cap pops up. That subtle "popping-up" is exactly what you're looking for.