ABSTRACT
This chapter recasts the line integral from calculus in complex notation. The result will be the complex line integral. The chapter discusses integrals on curves, the fundamental theorem of calculus along curves, and properties of integrals. It provides a set of exercises based on the complex line integral. The chapter also discusses the basis form of Cauchy Integral theorem. It is central and fundamental to the theory of complex functions. All of the principal results about holomorphic functions stem from this simple integral formula. A central fact about the complex line integral is the deformability of curves. The reasoning behind the deformability principle is simplicity itself. A topological notion that is special to complex analysis is simple connectivity. The Cauchy integral formula is derived from the Cauchy integral theorem.
