Integration from graph - Graph of $v(t)$ knowing the graph of $a(t)$

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We have the graph of accelation :

enter image description here

Can we get from that the graph of velocity ?

It holds that $v(t) = \int a(t)\, dt$ right?

So in $[0,3]$ where $a$ is increasing, i.e. $v'(t)>0$, the function $v(t)$ is convex.

In $[3,5]$ where $a(t)$ is constant, i.e. $v'(t)=6$, the function $v(t)$ is linear, $v(t)=6t$.

In $[5,8]$ where $a(t)$ is decreasing, i.e. $v'(t)<0$, the function $v(t)$ is concave.

Is everything correct so far?

Is that all or do we get more information from the first graph for the second one?

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You know (from elementary integration) that the graph of $v(t)$ is a parabola in $[0,3]$. You know that it then becomes a straight line in $[3,5]$, and then is a parabola with negative quadratic coefficient in the interval $[5,8]$. Assuming $v(0)=0$, but be aware that the reality will differ from the following graph by at most a constant term:

Graph

I use Desmos' numerical integration just to demonstrate - it is actually very easy to integrate this yourself. The following functions were based on your graph:

Functions