While the use of Lyapunov function candidates of integrator backstepping has been extensively studied in the litterature, little research has been conducted regarding the applicability of the so-called incremental stability approaches. This note addresses the problem of the use of an incremental approach, contraction theory, to the integrator backstepping design on the methodological aspect. After briefly recalling basic results from contraction theory, a full contraction-based integrator backstepping procedure is presented. An example is given to illustrate the approach.