How do i find this position time graph from a velocity time graph I have below the solution to the question i posted but the problem is i don't know how to do it. I know it is using integration but how were the separate points obtained?  thanks 
It is question b by the way. 


 A: Hint: Change in position over a specific time period is the integral of velocity over that time period.
A: There are a few geometrical facts about these kinds of diagrams that can be helpful.
First, as you are aware, the position is the integral of the velocity.
(The constant of integration is determined by the initial position.)
The integral of a constant $c$ is a linear function
(which plots as a straight line)
and the integral of a linear function is a quadratic function
(which plots as a parabola).
In places where the graph of the velocity is an upward sloping line,
you get a parabola curved upward (cup-shaped).
Where the graph of the velocity is a downward sloping line,
you get a parabola curved downward (arch-shaped).
Where the velocity is positive the position graph rises, and where the
velocity is negative the position graph falls.
Where the velocity crosses the axis (a transition through $v=0$),
the graph of the position changes direction (from rising to falling
or from falling to rising).
In your case, you have


*

*a negative but upward sloping velocity from $0$ to $2$,

*positive and upward sloping (at the same slope) from $2$ to $4$, 

*horizontal from $4$ to $6$,

*sloping downward from $6$ to $8$, and

*horizontal again from $8$ to $10$.


So the corresponding position graph has


*

*a part of a parabola that is decreasing but curving upward from $0$ to $2$;

*the "bottom" of that parabola at $t=2$ (where $v=0$);

*a continuation of the same parabola from $2$ to $4$, but this part is increasing;

*a straight line from $4$ to $6$;

*a part of a parabola from $6$ to $8$ that is increasing but curved downward;

*the "top" of that parabola at $t=8$ (where $v=0$);

*a straight line (horizontal, because $v=0$) from $8$ to $10$.


Also, the straight segment between the two parabolic arcs has the same slope as the end
of the first arc and the beginning of the second arc,
because the final velocity of the first arc equals the initial velocity 
of the second arc and both are equal to the velocity at all times in between.
