Maintenance costs M(t) in a factory increase as plant and equipment get older. Given the rate of increase in maintenance costs in dollars per year M’(t) = 75t2 + 9000, where t is the number of years, find the total maintenance costs of the factory from 4 to 6 years.

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M(6) M(4) = (751 +9000) dt =(2513 +90001)=21, 800