While Euclidean geometry allows us to find the areas of simpler regions such as polygons and ellipses, integration allows us to find the area bounded by arbitrary curves. The integral of a real-valued function over an interval is namely a measure of the area between the graph of the function and the \(x\)-axis over this interval.
Integration and differentiation remain the two main operations of calculus. Although finding areas and finding tangent slopes may seem totally unrelated, the discovery of their connection was made in the 17th century. This connection is given below, in the Fundamental Theorem of Calculus. The importance and utility of this theorem can not be overemphasized.