The Cauchy Integral is a fundamental theorem in complex analysis, named after the mathematician Augustin-Louis Cauchy. It states that if a function is holomorphic (complex differentiable) within and on some simple closed curve, the integral of that function over the curve is zero. This result is crucial for understanding the behavior of complex functions. Additionally, the Cauchy Integral formula provides a way to evaluate integrals of holomorphic functions. It states that if a function is holomorphic inside a closed curve, the value of the function at any point inside the curve can be expressed as an integral over the curve. This formula is essential for many applications in mathematics and physics.