Chapter 5.5, Problem 72E

Maintenance costs. Maintenance costs for an apartment house generally increase as the building gets older. From past records, the rate of increase in maintenance costs (in dollars per year) for a particular apartment complex is given approximately by

     $M^{\prime }\left(x\right)=f\left(x\right)=90x^2+5,000$

where x is the age of the apartment complex in years and M(x) is the total (accumulated) cost of maintenance for x years. Write a definite integral that will give the total maintenance costs from the end of the second year to the end of the seventh year, and evaluate the integral.