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The book consist of nine chapters. In chapter 1, we have discussed indefinite integration which includes basic terminology of integration, methods of evaluating the integration of several types as well as Integration of Rational and Irrational functions. Chapter 2 deals with the introduction and properties of definite integrals as well as summation of series. While chapter 3 deals with the Reduction formula of several types. In chapter 4, we have discussed introduction of Beta and Gamma functions, transformation, reduction, and relations of Beta and Gamma functions. In chapter 5, we have discussed the evaluation of double integral in cartesian and polar coordinates, change of order of integration, applications, evaluation of triple integral, Dirichlet’s Integral. While in chapter 6, we have discussed introduction and convergence of improper integrals. In chapter 7, Areas of curves in cartesian and polar coordinates are discussed. While in chapter 8, Rectification, Volume, and Surface of Solid Revolution in cartesian, polar and parametric equation also Intrinsic equation in cartesian, polar and parametric equation are discussed. Chapter 9 deals with Leibnitz’s differentiation under integral sign. Integral calculus is a branch of applied mathematics concerning mathematical models (mathematical methods and techniques) that are typically used in sciences, engineering, and industry. Brief Contents Integration of Rational Irrational Fractions • Definite Integral • Reduction Formula • Beta and Gamma Functions • Multiple Integrals • Improper Integrals • Rectification, Volume and Surface of Solid Revolutions • Differentiation Under Integrals Sign.