An integral is a mathematical object that can be interpreted as an area or a generalization of area. Integrals, together with derivatives, are the fundamental objects of calculus. Other words for integral include antiderivative and primitive. The Riemann integral is the simplest integral definition and the only one usually encountered in physics and elementary calculus. The study of integral calculus includes: integrals and their inverse, differentials, derivatives, anti-derivatives, and approximating the area of curvilinear regions. Integration is an important function of calculus, and introduction to integral calculus combines fundamental concepts with scientific problems to develop intuition and skills for solving mathematical problems related to engineering and the physical sciences. The book provides a solid introduction to integral calculus and feature applications of integration, solutions of differential equations, and evaluation methods. This book explores the integral calculus and its plentiful applications in engineering and the physical sciences. A basic understanding of integral calculus combined with scientific problems, and throughout, the book covers the numerous applications of calculus as well as presents the topic as a deep, rich, intellectual achievement. The needed fundamental information is presented in addition to plentiful references.