I really hope you're thinking of calculating digital signals.
Then it's pretty easy to do integration and differentation.
For digital signal processing the integral over a period of time becomes the sum of the sampled digital values over this period of time,
and the differential becomes the difference of two consecutive digital values at a certain point of time.
That means, that it's enough to add a series of digital values and shift the result back into the right range (integral), or calculate the difference of two digital values (differential).
Both procedures belong to the most favored tasks of a standard 8051.