  Given a 1-parameter family of 1-forms $\g(t)= \g_0+t\g_1+...+t^n\g_n$,
consider the condition $d\g(t)\wedge\g(t)=0$ (of integrability for the
annihilated by $\g(t)$ distribution $w(t)$). We prove that in order that this
condition is satisfied for any $t$ it is sufficient that it is satisfied for
$N=n+3$ different values of $t$ (the corresponding implication for $N=2n+1$ is
obvious). In fact we give a stronger result dealing with distributions of
higher codimension. This result is related to the so-called Veronese webs and
can be applied in the theory of bihamiltonian structures.
