Yes. A definite integral is often an accumulation of something over time. For example, if f(t) tells you how fast you are accumulating stuff (money, distance, whatever) at each moment of time t, then the integral of f(t) over [a,b] tells you the the total amount of stuff you've accumulated over during the time period [a,b]. For example, if f(t) is speed, then the integral of f(t) gives you the total distance traveled. If f(t) tells you how fast you are making money, then the integral of f(t) tells you how much money you made.

is your speed at each moment in time, then f(t) is essentially telling you how much distance you are accumulating (i.e., how far you've traveled) from moment to moment. So the integral of f(t) from [0,10] tells you the total distance you've accumulated during the interval [0,10].

Likwise, if f(t)