Question 1097281
You have to integrate the absolute value of the velocity from time {{{t=0}}} to {{{t=7}}}. 
You use the absolute value if you want to get the distance traveled else you will only get the displacement of the particle. 
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{{{S=int(abs(V),dt)=int(abs(t^3-12t^2+35),dt)=int((t^3-12t^2+35),dt,0,T)+int((-t^3+12t^2-35),dt,T,7)}}}
where {{{T=1.858}}}.