Integral inequalities of Ostrowski type are developed for n−times differentiable mappings, with multiple branches, on the Lp (1 < p < ∞) norm. Some particular inequalities are also investigated, which include explicit bounds for perturbed trapezoid, midpoint, Simpson's, Newton-Cotes and left and right rectangle rules. The results obtained provide sharper bounds than those obtained by Dragomir [6] and Cerone, Dragomir and Roumeliotis [3] .