This book is an “Integral Calculus” for graduate and Post graduate students. The basic idea of Integral Calculus along with the many examples is discussed in this book. This book “Integral Calculus” is consists of seven chapters, we have discussed topics: Reduction formulae, Beta and Gamma functions, Qudrature, Rectification, Volumes and surfaces of solids of revolution, Pappus ( ii ) theorem, Double and triple integrals, Change of order of integration, Dirichlet’s and Liouville’s integral formulae. Some important definition, theorems and examples.