$[10pts.]$

The volume $V(in$ liters$)of$ air $in$ the lungs during $a5$ second respiratory cycle $is$ given $by$ the model

$V(t)=0\mathrm{.}1729t+0\mathrm{.}1522t^2-0\mathrm{.}0374t^3+sin(\frac{t}{5})$ where $tis$ the time $in$ seconds. Set $upan$ integral $to$ find the

average volume $of$ air $in$ the lungs during one respiratory cycle. Show all detail $to$ integrate manually, including

any change $of$ bounds $(where$ appropriate$).$