Suppose we have a material point. If it is moving from position $X_0$ with initial velocity $V_0$ and constant acceleration $A$, then from elementary physics course I remember that its movement is described by the equation
$$X(t) = X_0 + V_0t + At^2/2.$$
Now, my question is, what is the equation of the movement of the material point if its acceleration is an arbitrary function of $t$: $A(t)$. Is it simply:
$$X(t) = X_0 + V_0t + A(t)t^2/2,$$
or is it more complicated than that? From the looks of $At^2/2$ I have a suspicion that integrals may be involved.