1. **Problem Statement:** Evaluate the Riemann sum for the function $f(x)$ on the interval $[1,5]$ using right endpoints as sample points. 2. **Understanding the Riemann Sum:** The Riemann sum with right endpoints is given by $$\sum_{i=1}^n f(x_i) \Delta x$$ where $x_i$ are the right endpoints of each subinterval and $\Delta x$ is the width of each subinterval. 3. **Given Data:** The subintervals are $[1,2], [2,3], [3,4], [4,5]$ with right endpoints at $x=2,3,4,5$. 4. **Function Values at Right Endpoints:** - $f(2) \approx 3.00$ - $f(3) \approx 2.36$ - $f(4) \approx 2.86$ - $f(5) \approx 1.00$ 5. **Calculate $\Delta x$:** Each subinterval has width $$\Delta x = 2 - 1 = 1$$ 6. **Compute the Riemann Sum:** $$\text{Riemann sum} = \sum_{i=1}^4 f(x_i) \Delta x = (3.00 + 2.36 + 2.86 + 1.00) \times 1 = 9.22$$ 7. **Interpretation:** The Riemann sum approximates the area under the curve $f(x)$ from $x=1$ to $x=5$ using rectangles with heights given by the function values at the right endpoints. **Final answer:** $$\boxed{9.22}$$