  In this article we give an expression of the motivic Milnor fiber at infinity
and the motivic nearby cycles at infinity of a polynomial $f$ in two variables
with coefficients in an algebraic closed field of characteristic zero. This
expression is given in terms of some motives associated to the faces of the
Newton polygons appearing in the Newton algorithm at infinity of $f$ without
any condition of convenience or non degeneracy. In the complex setting, we
compute the Euler characteristic of the generic fiber of $f$ in terms of the
area of the surfaces associated to faces of the Newton polygons. Furthermore,
if $f$ has isolated singularities, we compute similarly the classical
invariants at infinity $\lambda_{c}(f)$ which measures the non equisingularity
at infinity of the fibers of $f$ in $\mathbb P^2$, and we prove the equality
between the topological and the motivic bifurcation sets and give an algorithm
to compute them.
