Unusual breadth of knowledge about the theory of fuzzy sets created a tendency for writing an up-to-date researches on tools for fuzzy analysis. In recent years, important development in fuzzy theory and its applications have taken place. In this thesis, some principle theorems and definitions as well as some properties and remarks of different kinds of fuzzy integration have been presented and discussed. In our work, some numerical solutions of different kinds of fuzzy integration, supported by computational algorithms, necessary theorems, remarks and some illustration examples, as well as comparisons if possible, have been developed. Integration is made on the following numerical fuzzy integration procedures: 1. The numerical solution of fuzzy integration of crisp valued function over fuzzy interval using the domain partitions of the membership function of the fuzzy interval. 2.The numerical solution of fuzzy integration of crisp valued function over fuzzy interval using the range partitions of the membership function of the fuzzy interval. 3.The numerical solution of fuzzy integration of fuzzy function over the crisp interval. 4.The numerical solution of fuzzy integration of bunch fuzzy function over the crisp interval. 5.The numerical solution of fuzzy integration of the LR-type fuzzy function over the crisp interval. 6.The numerical solution of fuzzy integration of LR-type fuzzy function over the LR-type representation of fuzzy interval. Some conclusions, remarks and future work have also being suggested.