Use limits to evaluate the integral.

Split up the interval [0, 2] into n equally spaced subintervals:

Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,

where . Each interval has length .

At these sampling points, the function takes on values of

We approximate the integral with the Riemann sum:

Recall that

so that the sum reduces to

Take the limit as n approaches infinity, and the Riemann sum converges to the value of the integral:

Just to check:

6, 10

9, -13

12, -21

18, -23

step-by-step explanation:

you just add 6 to the x-coordinate and subtract 10 from the y-coordinate.