1. The problem asks about the result of a Riemann sum. 2. A Riemann sum is a method for approximating the total area under a curve on a graph, which represents the integral of a function. 3. The formula for a Riemann sum is $$S = \sum_{i=1}^n f(x_i^*) \Delta x$$ where $f(x_i^*)$ is the function value at a chosen point in the $i$th subinterval and $\Delta x$ is the width of each subinterval. 4. Important rules: - The more subintervals $n$ you use, the better the approximation. - The choice of sample points $x_i^*$ (left endpoint, right endpoint, midpoint) affects the sum. 5. As $n \to \infty$ and $\Delta x \to 0$, the Riemann sum approaches the exact value of the definite integral $$\int_a^b f(x) \, dx$$. 6. Therefore, the result of a Riemann sum is an approximation of the definite integral of the function over the interval $[a,b]$. 7. In summary, the Riemann sum gives an approximate value for the area under the curve, and in the limit, it equals the definite integral.