  This paper provides a full characterization of the value function and
solution(s) of an optimal stopping problem for a one-dimensional diffusion with
an integral criterion. The results hold under very weak assumptions, namely,
the diffusion is assumed to be a weak solution of stochastic differential
equation satisfying the Engelbert-Schmidt conditions, while the (stochastic)
discount rate and the integrand are required to satisfy only general
integrability conditions.
