How to transfer data from LogicMonitor to other tools?

If you want to pull the data at set intervals then use a script and the REST API to extract the data.  If you want data pushed when something happens, like when an alert occurs, then use an integration.  The HTTP integration is very useful for pushing data to other systems that have webhooks to receive data.

If you want historial data, graph data for example, then you'll need to pull that using the REST API, because there's no way (that I know of) to push that using an integration.