  In the framework of a flat Friedmann-Lema{\^\i}tre-Robertson-Walker (FLRW)
geometry, we present a nonsingular model (no big bang singularity at finite
time) of our universe describing its evolution starting from its early
inflationary era up to the present accelerating phase. We found that a
hydrodynamical fluid with nonlinear equation of state could result in such a
non singular scenario, which after the end of this inflationary stage, suffers
a sudden phase transition and enters into the stiff matter dominated era, and
the universe becomes reheated due to a huge amount of particle production.
Finally, it asymptotically enters into the de Sitter phase concluding the
present accelerated expansion. We show that the background providing an
inflationary potential leads to a power spectrum of the cosmological
perturbations which fit well with the latest Planck estimations. At the end, we
compared our viable potential with some known inflationary quintessential
potentials, which shows that, our model is an improved version of them because
it contains an analytic solution that allows us to perform analytic
calculations.
