  Here we analysed a particular type of $F(R)$ gravity, the so-called
exponential gravity which includes an exponential function of the Ricci scalar
in the action. Such term represents a correction to the usual Hilbert-Einstein
action. By using Supernovae Ia, Barionic Acoustic Oscillations, Cosmic
Microwave Background and $H(z)$ data, the free parameters of the model are well
constrained. The results show that such corrections to General Relativity
become important at cosmological scales and at late-times, providing an
alternative to the dark energy problem. In addition, the fits do not determine
any significant difference statistically with respect to the $\Lambda$CDM
model. Finally, such model is extended to include the inflationary epoch in the
same gravitational Lagrangian. As shown in the paper, the additional terms can
reproduce the inflationary epoch and satisfy the constraints from Planck data.
