How do I integrate a Media library to Image Field? I have a image upload element field in my content type. I need to open a media library when I click on browse. My expectation is to select an image which I have already uploaded before. So I don't have to upload the same image again and again.

I've searched but I couldn't find a module for media library in Drupal 8. They are saying it is in the core of Drupal 8. I couldn't find it too. Is there an easy way to do this? Simply what I wanted is a library like in the image.(this is the media library in wordpress)
You are looking for entity_browser. 

Setup isn't that easy, so you may want to use an existing browser like media_entity_browser as a starting point.

The media library as shown in your image can be found at admin/content/media, but it's not that helpful when it comes to reusing images on a node.