  We formulate indefinite integration with respect to an irregular function as
an algebraic problem and provide a criterion for the existence and uniqueness
of a solution. This allows us to define a good notion of integral with respect
to irregular paths with Hoelder exponent greater than 1/3 (e.g. samples of
Brownian motion) and study the problem of the existence, uniqueness and
continuity of solution of differential equations driven by such paths. We
recover Young's theory of integration and the main results of Lyons' theory of
rough paths in Hoelder topology.
