  In this paper we give an upper bound for the number of integral points on an
elliptic curve E over F_q[T] in terms of its conductor N and q. We proceed by
applying the lower bounds for the canonical height that are analogous to those
given by Silverman and extend the technique developed by Helfgott-Venkatesh to
express the number of integral points on E in terms of its algebraic rank. We
also use the sphere packing results to optimize the size of an implied
constant. In the end we use partial Birch Swinnerton-Dyer conjecture that is
known to be true over function fields to bound the algebraic rank by the
analytic one and apply the explicit formula for the analytic rank of E.

Number Theory