Over the last few years, the use of special functions has increased exponentially, especially in Physical Sciences and Engineering due to its wide applications. A lot of research work has recently come up on the study and development of the Special functions and now stands on fairly firm footing through the research contributions of various researchers. This Book is an invention both to the interested scientists and the engineers. It presents a throughout introduction to the real results of special function. It is also devoted to the applications of mathematical sciences and engineering problems. The aim of the present investigation is to obtain certain new and interesting integral formulas involving Fox H- function, General class of polynomials and some other special functions. In the last chapter we discuss about the Graphical interpretation of some special function with MATLAB coding.