Is clearing my history enough?

Clearing your browser history only deletes the list of the websites and pages you visited. What else does your browser keep track of any undeleted history: To find out, press Ctrl+Shift+Delete (Windows) or CMD+Shift+Delete (macOS), go to the Advanced tab.

Does this go to trash directly? in recycle bin?

It will automatically clear your history. Make sure to delete earlier as not to keep files long in your computer. Recycle bin is for apps, files, photos and videos saved in your computer.