export – How to trim a FBX animation file?

at first select all the objects with A

In case you want only specific objects to be exported, select those objects with Left-click, to add more objects to selection, hold Shift + Left-click

On the Timeline window you will see multiple white squares (keyframes)

By scrolling the MMB you zoom IN/OUT on the timeline

While hovering over the Timeline tab, hit B, a checkered cross will appear allowing for click and drag selection

Select the keyframes you want to delete

For further selection, hit B again and select another set of keyframes

And hit Delete

Then just navigate to File > Export > FBX

In case of exporting only selected objects, make sure you check the
Selected Objects checkbox

Done!

When imported again, you should only get the keyframes from the desired part.