If you're given some random integral to integrate, you probably won't be told whether it's improper or not. It might be improper because of badly behaved limits, a badly behaved function, or both. Either way, you can break it into smaller improper integrals, each of which is improper for only one reason.
Determine if the integral
converges or diverges.
Split the integral into a sum of integrals that are each improper for only one reason.