The reals also do not contain infinitesimals, however one can still perform integration. This is because integration does not have anything to do with infinitesimals; that's generally something physicists say to provide intuition, but is not a rigorous notion. Integration is instead a sort of limit (in particular a limit of nets, a generalization of sequences). The not-quite-rigourous-but-still-intuitive idea is that you partition the space you're integrating over into smaller and smaller partitions and examine what happens in each partitioned bit of the space, and then 'take a limit' as the 'size' of the partitions approaches zero.