A common problem in kinetic modeling of complex chemical reactions is that a rigorous description of the reaction system, e.g., based on elementary reactions, is not possible. This is because either the reaction involves too many reactions and intermediates or the reaction mechanism is not known in sufficient detail. Alternative data-driven modeling, e.g., using neural networks, normally demands large amounts of experimental data and has poor generalization capability. In such situations a combined physical and data-driven (i.e. hybrid) model may be attractive, that utilizes the specific advantages of both approaches while avoiding their disadvantages. This paper explains the procedure of hybrid modeling of integral (i.e. time-dependent) data by using examples from chemical kinetics. The benefits of the hybrid models are described in comparison to the limiting cases of purely physical and purely data-driven models. In general, the hybrid model surpasses the purely physical and neural network models in terms of a combined interpolation- and extrapolation-range criterion.