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Integral of single variable functions is an important issue in calculus. This problem is widely applied in many fields such as physics, economics, etc. Systems for automatic solving integral problems are necessary tools in education. They support students and teachers in learning and teaching. Current computer algebra systems such as Maple, Mathematica, etc can solve integral problems. However, they output the result only or are limited to give the complete solution. This paper presents a model for representing knowledge about single variable functions and proposes some algorithms for solving integral problem automatically. These algorithms mimic the human way of thinking and produce the solution that explains the calculus process.