  Let P(x,y) be a rational polynomial and k in Q be a generic value. If the
curve (P(x,y)=k) is irreducible and admits an infinite number of points whose
coordinates are integers then there exist algebraic automorphisms that send
P(x,y) to the polynomial x or to x^2-dy^2. Moreover for such curves (and
others) we give a sharp bound for the number of integral points (x,y) with x
and y bounded.
