Consider the integral given by

${\displaystyle \underset{-1}{\overset{5}{}}}(2+3x)dx$

Using the following definition of the integral

${\displaystyle \underset{a}{\overset{b}{}}}f(x)dx=\underset{n}{lim}{\displaystyle \underset{i=1}{\overset{n}{}}}f(x_i)x$

where $x_i$ are right hand endpoints.

$($a$)$ Determine $x$ and $x_i.$

$$

$x=$

$x_i=$

$($b$)$ Using the definition mentioned above, evaluate the integral.

Value of integral: $$