This has been returned as homework and I have to make corrections. My teacher isn't very helpful and I can't afford a tutor.
When satellites circle closely around a planet or moon, the gravitational field surrounding the celestial body both increases the satellite’s velocity and changes its direction in an orbital move called a “slingshot.” Let’s say that a ship executing this maneuver has position $s(t) = t^3 - 2t^2 - 4t + 12$, where $t$ is in hours and $s(t)$ represents thousands of miles from Earth. What is the total distance traveled by the craft during the first five hours?