Find the average value of $f(x)=\frac{2(x^2+1)}{x^2}$ on $1,3.$

$(1$ point$)$

$2$

$\frac{8}{3}$

$3$

$\frac{28}{9}$

$\frac{16}{3}$

Which definite integral can be expressed as $\underset{||P||0}{lim}{\displaystyle \underset{k=1}{\overset{n}{}}}(\frac{1}{4}{c}_k^3-3c_k+5)x_k,$ where $P$ is any partition of $2,5?(1$ point$)$

${\displaystyle \underset{2}{\overset{5}{}}}(\frac{3}{4}{x}^2-3)dx$

${\displaystyle \underset{5}{\overset{2}{}}}(\frac{3}{4}{x}^2-3)dx$

${\displaystyle \underset{5}{\overset{2}{}}}(\frac{3}{4}{x}^3-3x^2+5)dx$

${\displaystyle \underset{2}{\overset{5}{}}}(x^4-3x^2+5)dx$

${\displaystyle \underset{2}{\overset{5}{}}}(\frac{1}{4}{x}^3-3x+5)dx$