Work through the following steps to evaluate ${\displaystyle \underset{0}{\overset{7}{}}}(x^{2}1)dx.$

a$)$ We know that $a=$ and $b=$

b$)$ Using $n$ subintervals, $x=$

c$)$ Assume that the sample points in each interval are right endpoints. Find the following sample points:

$x_1=$

$x_2=$

$x_3=$

In general, the $i$ th sample point is $x_i=$ Note: your answer will be an expression in terms of i and $n.$

d$)$ Now find the sum of the areas of $n$ approximating rectangles. Note: your answer will be an expression in terms of $n.$