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@article{203111,
        author = {Dr. Amrish Kumar Srivastav},
        title = {A Study on the Concept and Integrability Conditions of Riemann Integration},
        journal = {International Journal of Innovative Research in Technology},
        year = {2026},
        volume = {12},
        number = {12},
        pages = {9279-9282},
        issn = {2349-6002},
        url = {https://ijirt.org/article?manuscript=203111},
        abstract = {Bernhard Riemann integration constitutes one of the foundational concepts of mathematical analysis and plays a central role in the development of modern calculus, functional analysis and applied mathematics. This paper presents a comprehensive study of the theory and applications of Riemann integration, focusing on its conceptual framework, integrability conditions and mathematical significance. The study examines the construction of the Riemann integral through partitions, upper and lower sums and the limiting process that establishes the existence of an integral for bounded functions defined on closed intervals. Particular emphasis is given to the criteria for Riemann integrability, including continuity, monotonicity and the characterization of discontinuous functions.
By combining theoretical exposition with illustrative examples and applications, this study aims to provide a deeper understanding of Riemann integration and its enduring importance in pure and applied mathematics. The findings underscore the relevance of Riemann integration not only as a classical analytical tool but also as a gateway to advanced topics in real analysis, measure theory, differential equations and mathematical modeling.},
        keywords = {Riemann integration, monotonicity, measure theory, differential equation},
        month = {May},
        }