Some definite integrals can only be defined via limits. Such integrals are called improper integrals. We distinguish two types: a type where the interval of integration has infinite length and a type where the integrand is unbounded when it gets near one or two endpoints of the integration interval. For both types of improper we assume that the integrand is continuous except possibly in the endpoints of the integration interval. The only reason for this assumption is that we can be sure in this case that antiderivatives of the given integrand do exist.
If the improper integral exists, i.e., is a finite number, we say that the integral converges.
If the improper integral is plus or minus infinity, we say that the integral diverges.