  We use the local momentum space technique to obtain an expansion of the
Feynman propagators for scalar field and graviton up to first order in the
background curvature. The expressions for the propagators are cross-checked
with the past literature as well as with the expressions for the traced heat
kernel coefficients. The propagators so obtained are used to compute one-loop
divergences in the Vilkovisky-Dewitt's effective action for a scalar field
non-minimally coupled with gravity for an arbitrary spacetime metric
background. The Vilkovisky-DeWitt effective action is then compared with the
standard effective action in the limit $\kappa =0$, where $\kappa = 2/M_P$ in
terms of the Planck mass. The comparison yields the important result that
taking the limit $\kappa=0$ after computing the Vikovisky-DeWitt effective
action is not equivalent to computing the Vikovisky-DeWitt effective action for
the same theory in the absence of gravity.
