This presentation introduces integral algebra and shows how it can be used to simulate a dynamical system with interval uncertainties. These uncertainties, can be either on the initial state vector, on the time-dependent inputs, or on the evolution function. Compared to other techniques used for the guaranteed integration of differential inclusion, the presented approach does not require the use of a fixed-point Picard operator. Two test-cases related to robotics are presented to illustrate the efficiency of the approach.