Differentiation

Velocity ($v$) is the rate of change of displacement ($s$), therefore:

$v = \dfrac{ds}{dt}$

Acceleration ($a$) is the rate fo change of velocity ($v$), therefore:

$a = \dfrac{dv}{dt} = \dfrac{d^2s}{dt^2}$

Integration

Integration is the reverse process to differentiation, therefore:

$s = \displaystyle\int{v}~dt$

$v = \displaystyle\int{a}~dt$