How could the definite integral be used to determine profit over a given period?

Question

How could the definite integral be used to determine profit over a given period?

Answer 1

If P(t) = total profit after t years, then P(b) - P(a) is the change in profit from t = a years to t = b years.  

 

P(b) - P(a) = ∫P'(t)dt (from t = a to t = b).