The table gives the values of a function obtained from an experiment. Use them to estimate $\int_{0}^{\,6} {f(x)}\, dx$ using three equal subintervals with (a) right endpoints, (b) left endpoints, and (c) midpoints. $$\begin{array}{|c|c|c|c|c|c|c|c|}\hline x & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline f(x) & 9.3 & 9.0 & 8.3 & 6.5 & 2.3 & -7.6 & -10.5 \\ \hline \end{array}$$

(a) $R_3 =$

(b) $L_3 =$

(c) $M_3 =$

(d) If the function is known to be a decreasing function, can you say whether your estimates are less than or greater than the exact value of the integral?

? Less than the exact value Greater than the exact value Can't tell  1. $M_3$

? Less than the exact value Greater than the exact value Can't tell  2. $R_3$

? Less than the exact value Greater than the exact value Can't tell  3. $L_3$