Forget about Video to Gif from Imgur (limited to 15 seconds), or the softwares Free Video to GIF Converter, Free Video to JPG Converter and Gimp, ...

The best tool is to select the part of the video with avidemux, save it as a mpeg, or avi, or mp4.

Play the video with VLC or Media Player.

And record a selected area with ScreenToGif.