In the realm of mathematics, the evaluation of integrals plays a crucial role in various fields such as physics, engineering, and economics. Integrals represent the accumulation of quantities over a continuous range and are essential for understanding the behavior of functions and solving complex problems. Over the years, mathematicians and researchers have developed numerous techniques to evaluate integrals efficiently and accurately. This thesis consists of two parts. In the first part, we present some binomial identities, special numbers and polynomials as well as basic formulas related to ...