i think you are asking about the improper integrals..
this type of integrals should be evaluated in by using the limits ..
you should know how to take the limit of an improper integrals in correct way.
also, you should know the types of the improper integral which you are dealing with.
anyway at the end you will face a limit of specific function,
if the value of this limit is an finite number --> the integral converges.
if the value of this limit is not finite or D.N.E ---> the integral diverges.
also you should know that the impropet integral from 1 to infinity for /[(x)^p]
is convergent if p > 1
and divergent if p <1
try to search in google about improper integrals.