Answer is: option4

Solution:

Identify the right endpoints of each subinterval:

1. Right endpoint of \( [1, 3] \) is \( 3 \)
2. Right endpoint of \( [3, 5] \) is \( 5 \)
3. Right endpoint of \( [5, 8] \) is \( 8 \)
4. Right endpoint of \( [8, 10] \) is \( 10 \)

Use the function values at these right endpoints:

From the table:

1. \( f(3) = 12 \)
2. \( f(5) = 16 \)
3. \( f(8) = 23 \)
4. \( f(10) = 17 \)

Calculate the widths of each subinterval:

1. Width of \( [1, 3]: 3 - 1 = 2 \)
2. Width of \( [3, 5]: 5 - 3 = 2 \)
3. Width of \( [5, 8]: 8 - 5 = 3 \)
4. Width of \( [8, 10]: 10 - 8 = 2 \)

Apply the Right Riemann Sum formula:

\[ \text{Approximation} = \sum (\text{width of interval}) \times f(\text{right endpoint}) \] \[ = 2 \cdot f(3) + 2 \cdot f(5) + 3 \cdot f(8) + 2 \cdot f(10) \] \[ = 2 \cdot 12 + 2 \cdot 16 + 3 \cdot 23 + 2 \cdot 17 \] \[ = 24 + 32 + 69 + 34 = \boxed{159} \]

Final Answer Option D