Welcome to the annoying world of browsers that change their behavior from time to time, with no warning!

Here's what worked for me (Windows 10) when BOTH Chrome and Firefox stopped displaying PDFs directly, 

and instead asked for a place to download them.

Display PDFs in Chrome or Firefox

Firefox

Scroll down ...

Scroll down ...

No "Save" - just close the "Settings" tab

Chrome

This is an extension (not a "setting")

This is a "setting" (not an extension/plugin)

Close the tab

No "Save" - just close the "Extensions" tab

If you already have the extension, 

check to make sure it's turned ON:

Click to turn ON