1. The problem asks why the Riemann sum becomes exact as $n \to \infty$. 2. The Riemann sum approximates the area under a curve by dividing it into $n$ rectangles and summing their areas. 3. As $n$ increases, the width of each rectangle $\Delta x = \frac{b-a}{n}$ becomes smaller, making the approximation closer to the true area. 4. In the limit as $n \to \infty$, the width $\Delta x$ approaches zero, and the sum converges to the exact integral value. 5. This is because the sum effectively becomes the integral definition: $$\lim_{n \to \infty} \sum_{i=1}^n f(x_i^*) \Delta x = \int_a^b f(x) \, dx.$$