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FInd the integral or the area under the curve and you will have total distance.

Velocity is a vector speed is a magnitude.

Please see the axis, it's y=distance , x=time, it's NOT y=velocity , x=time!

in this case velocity is Dx/dt = velocity. In the x direction.

It's the same it's only giving you the distance throughout the total time.

Perhaps you should read this
http://answers.yahoo.com/question/index?qid=20080906075747AABsnoO

Displacement as a straight line yes.

f(t) = 1/2 t + 9 ; t = [0,8)
= 2t + c ; t = (8,10]
havent the time to determine "c" tho