Riemann Integral: Significance and Limitations

This article basically defines the Riemann integral starting with the definition of partition of a closed interval. It throws a light on the importance and necessity of the Riemann condition of integralbility of a function and explains how the concept of R- integral only on the basis of upper and lower integral is not always practical. It has been suggested that a better rout is to abandon the Reimann integral for Lebesgue integral in real analysis and other fields of mathematical science.