An engineer knows $a\left(t\right)$ and wants to reconstruct $x\left(t\right)$. Which sequence of operations is required, along with the needed information?

Differentiate $a\left(t\right)$ to get $v\left(t\right)$, then differentiate $v\left(t\right)$ to get $x\left(t\right)$, using one initial condition

Integrate $a\left(t\right)$ once to get $x\left(t\right)$, using any final velocity value

Differentiate $a\left(t\right)$ once and then integrate once, because the operations cancel exactly

Integrate $a\left(t\right)$ to get $v\left(t\right)$, then integrate $v\left(t\right)$ to get $x\left(t\right)$, using enough initial conditions to determine both constants