What are some examples of MSI (Medium-Scale Integration) circuits that are used for doing arithmetic?
Probably one of the most widely used MSI arithmetic circuits is the 74283 4-bit adder. Several of them could be wired in series to perform 8-bit, 16 bit or even 32-bit operations.

This is the internal circuitry of a 74HC283 from Philips:



which  shows it is clearly of MSI complexity.

Another popular chip was the 74181 bit-slice arithmetic logic unit. It is a step up from a simple 4-bit adder, and could perform all the traditional add / subtract / decrement operations with or without carry, as well as AND / NAND, OR / NOR, XOR, and shift.  Like the 74283, it could be ganged together to work with various word lengths.

This chip was used in the core of the CPU of such computers as the PDP-11 and VAX 11/780.  Here is its internal structure:



Unlike the 74HC283, I don't believe the 74181 is being made anymore.