Solve a Specific Antiderivative $(aka$ Initial Value$)$ Problem.

The rate $of$ change $of$ a company's total sales, $in$ millions $of$ dollars per month, after $t$ months $is$ given $by$

$s(t)=\frac{3}{4\sqrt[4]{t}}+\frac{0\mathrm{.}1}{\sqrt[\phantom{2}]{t}}+11$

After $6$ months, the company earned $89\mathrm{.}3236$ million dollars $in$ sales. Find a function representing the company's total sales after $t$ months. Note: $s(t)$

$is$ sometimes used $in$ place $of{S}^{\text{'}}(t)$ for the rate $of$ change $as$ the meaning $is$ the same: $s(t)=S^{\text{'}}(t).$

$S(t)=,$ millions $of$ dollars per month.