Use a right-hand sum with the sub-intervals indicated by the data in the table to estimate the area between the graph of *f* and the *x*-axis on the interval [-10,1].

Answer

From the table we can see that the sub-intervals we need to use are

[-10,-7], [-7,-6], [-6,-2], and [-2,1].

These have lengths 3, 1, 4, and 3 respectively.

On the sub-interval [-10, -7] the rectangle has height *f* (-7) = 10 and width 3, so its area is 30.

On the sub-interval [-7, -6] the rectangle has height *f* (-6) = 7 and width 1, so its area is 7.

On the sub-interval [-6,-2] the rectangle has height *f* (-2) = 2 and width 4, so its area is 8.

On the sub-interval [-2, 1] the rectangle has height *f* (-1) = 1 and width 3, so its area is 3.

We estimate that the area between the graph of *f* and the *x*-axis on [-10,1] is

30 + 7 + 8 + 3 = 48.