  In this paper we are interested in obtaining the exact expression and the
study of the constant sign of the Green's function related to a second order
perturbed periodic problem coupled with integral boundary conditions at the
extremes of the interval of definition.
  To obtain the expression of the Green's function related to this problem we
use the theory presented in \cite{CLY} for general non-local perturbed boundary
value problems. Moreover, we will characterize the parameter's set where such
Green's function has constant sign. To this end, we need to consider first a
related second order problem without integral boundary conditions, obtaining
the properties of its Green's function and then using them to compute the sign
of the one related to the main problem.
