Discrete Time Integrator (VS) Continuous Integrator
A 1st order analogue integrator is usually made from an op-amp and has two components that define the integration constant; a resistor and a capacitor: -



The picture above shows the equivalent digital implementation.

T is the sampling rate and C and R are the same as in the analogue integrator.

Note the negative sign in the first gain block - this is only needed if exactly mimicking the behavior of an analogue integrator (which naturally inverts). 

To make a 2nd order integrator cascade two of these "circuits".