  Using modified gravity with non-linear terms of curvature, $R^2$ and $R^{(r
+2)}$ (with $r$ being the positive real number and $R$ being the scalar
curvature), cosmological scenario,beginning at the Planck scale, is obtained.
Here, a unified picture of cosmology is obtained from $f(R)-$ gravity. In this
scenario, universe begins with power-law inflation, followed by deceleration
and acceleration in the late universe as well as possible collapse of the
universe in future. It is different from $f(R)-$ dark energy models with
non-linear curvature terms assumed as dark energy. Here, dark energy terms are
induced by linear as well as non-linear terms of curvature in Friedmann
equation being derived from modified gravity.It is also interesting to see
that, in this model, dark radiation and dark matter terms emerge spontaneously
from the gravitational sector. It is found that dark energy, obtained here,
behaves as quintessence in the early universe and phantom in the late universe.
Moreover, analogous to brane-tension in brane-gravity inspired Friedmann
equation, a tension term $\lambda$ arises here being called as cosmic tension.
It is found that, in the late universe, Friedmann equation (obtained here)
contains a term $- \rho^2/2\lambda$ ($\rho$ being the phantom energy density)
analogous to a similar term in Friedmann equation with loop quantum effects, if
$\lambda > 0$ and brane-gravity correction when $\lambda < 0.$
