>incident response is one area where we are frequently confronted with synthesis problems: we have to understand how the pieces normally fit together in order to make sense of what is currently going wrong.

I'm not sure I can accept without further clarification equating that with synthesis. Normally in incident response, you start with a full system where in principle any root cause is possible and gradually reduce scope until finding the solution.

For me integration could be used for say taking three adhoc solutions and designing a general one that fits all, or merging two different services after a company merge. But anything debugging is very clearly analytic.