# Integrating function of acceleration to obtain displacement

Lets assume a function a = |sin t| for acceleration over time. If we integrate it, we get instantaneous velocity. Now i have taken a limit for time. How will this graph look like?

I have been told that integrating a function provides me with the area under the curve. If i represent this in a linear way (without area), do i get a function which has a periodic increase in rate of change? Now if i want the displacement, I would integrate the function for velocity. As i now have the function for displacement, how will this graph look like?

I understand that it will simply be a graph which increases just like velocity does, but since the graph a = |sin t| after integration, gives us the area under it for velocity, is it possible to represent the displacement in the same graph? Just like velocity was in an a-t graph? If i look at it in terms of dimensions, Its obvious why this happens, its simply because velocity = m/s. And assuming t is in seconds and acceleration in m/s^2, area would naturally give us velocity. But to obtain displacement, i would need to multiply the square of time with the acceleration.

What implications does this have on the graph?

Thank you.