  In the present model, a unified picture of cosmology from early inflation to
late acceleration is obtained from $ f(R)-$ gravity with non-linear terms $ R^2
$ and $ R^5 $ of scalar curvature $R$. It is discussed that elementary
particles and radiation are produced during early inflation. The emitted
radiation thermalizes the universe to a very high temperature $ \sim
10^{18}{\rm GeV}$. The exit of the universe from inflationary phase is followed
by deceleration due to radiation-dominance heralding the standard cosmology
with background radiation having the initial temperature $ \sim 10^{18}{\rm
GeV}$. It is found that dark matter is induced by curvature and baryonic matter
is produced during inflation. Radiation-dominated phase is followed by
deceleration due to matter-dominance. The curvature-induced phantom dark energy
dominates at the red-shift $ z = 0.303 $ causing the late acceleration. It is
found that the universe will collapse in future. Further, it is investigated
that back-reaction of quantum particles produced near the collapse time can
avoid cosmic collapse and the universe will escape to revival of the state of
early universe.
