A car$-$leasing firm must decide how much to charge for maintenance on the cars it leases. After careful study, the firm

determines that the rate of maintenance, $M(x),$ on a new car will be approximately $M(x)=50(1+x^2)$ dollars

per year, where $x$ is the number of years the car has been in use. What total maintenance cost can the company

expect for a $2-$year lease? What minimum amount should be added to the monthly lease payments to pay for

maintenance on a $2-$year lease?

Write a definite integral to find the total maintenance cost for a $2-$year lease.

${\displaystyle \underset{0}{\overset{2}{}}}(50(1+x^2))dx$

The total maintenance cost the company can expect on a $2-$year lease is $

$($Round to the nearest cent as needed.$)$