<p>This paper introduces a new method for solving linear Fredholm integral equations of the second kind by utilizing Bernoulli polynomials combined with improved block-pulse functions. The main goal is to create a numerical method that is both efficient and accurate that leverages the properties of Bernoulli polynomials for approximating the solution while utilizing the flexibility and simplicity of block-pulse functions for discretization. The improved block-pulse function enhances the representation of the solution by offering better convergence and accuracy. By combining these two mathematical tools, the method provides a robust framework for addressing Fredholm integral equations, which are commonly encountered in areas like physics, engineering, and applied mathematics, the proposed method's effectiveness is illustrated through multiple examples, highlighting its capacity to provide precise and computationally efficient solutions. The findings indicate that using Bernoulli polynomials alongside improved block-pulse functions shows potential for solving complex integral equations with great accuracy.</p>