This book is designed as an advanced guide of integral calculus. It covers the following topics: indefinite integral, basic integrals, methods: decomposition, change of variable, integration by parts, trigonometric, rational functions and partial fractions, substitutions to rationalize, definite integral, area by mean of inscribed and circumscribed polygons, Riemann sums, integrability theorem, first fundamental theorem, second fundamental theorem, integral as area under the curve, area between two curves, mean value theorem, theorem of symmetry and periodicity, volumes of revolution: discs, washers, cylindrical shells, arc length and lateral surface, indeterminate forms of type 0/0 and ¿ / ¿, improper integrals: infinite limits of integration, infinite integrands, integrands with functions that are infinite at an interior point, derivatives and integral of transcendental functions: logarithmic, exponential, trigonometric, hyperbolic, inverse, introduction to differential equations, miscellaneous exercises. This is including the deduction of many formulas to clarify the concepts and meet all the needs of the students to reach the fundamentals of integral calculus.