Integrals: Total Distance

he velocity function *v*(*t*) (in meters per second) is given for a particle moving along a line.

$\displaystyle v(t)=3t-7, 0\leq t\leq 3$

a) Find the displacement *d*1 traveled by the particle during the time interval given above.

b) Find the total distance *d*2 traveled by the particle during the time interval given above.

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I found a) is -7.5, but I'm a bit confused by integrals. I don't understand how calculating the area under the graph finds "displacement" (I'm a bit confused about what displacement actually means in this kind of a question). And I have no idea how to approach part b (it doesn't even sound like it should involve integrals).

Also, if anyone has a particularly firm grasp on this, and would be willing to write a brief paragraph explaining why the Fundamental Theorem of Calculus works (not a proof, just an explanation, or a push in the right direction for my own mind), I would really appreciate you for that.