Chapter 5.5, Problem 87E

Oil production. Using production and geological data, the management of an oil company estimates that oil will be pumped from a producing field at a rate given by

     $\begin{array}{cc}R\left(t\right)=\frac{100}{t+1}+5& 0\le t\le 20\end{array}$

where R(t) is the rate of production (in thousands of barrels per year) t years after pumping begins. Approximately how many barrels of oil will the field produce during the first 10 years of production? From the end of the 10th year to the end of the 20th year of production?