It is fact that some users are too much habituated in searching Google from the search bar in Google chrome or Firefox. If you want the same in Internet explorer, you are frustrated. The Internet Explorer from Microsoft uses Bing as their default search engine. So whatever you will type in the IE search bar, it will search for that keyword in Bing.
But, there is an option in Internet explorer to change the default search engine and you can set it to Google. Let us take a look at the search option in this heritage browser.
Click on Tools and select Internet Options from the menu.

In the Internet Options window, click on Settings button under the “Search” category.

Here, you can see only one search engine has been provided. So at this moment, you have nothing to do with that.

If you want Google as the default search engine in Internet Explorer, go for the following steps.
What you have to do first is add the search engine add-on for Google search in Internet Explorer. Clicking this link will show a list of addons. Click on the addon, named as “Google Search”.
It will integrate the addon into your Internet explorer.
Once you successfully install that addon into Internet Explorer, go to the Search setting as you did earlier. Now, you can find that the Google has been added to the list. Select Google and click on “Set as default” button.

You are done! You can search Google directly from the search bar in Internet Explorer.
Search Google from right-click menu in Internet Explorer
There is another way to search Google in Internet Explorer. Select any word or phrase and search the Google with that from right-click menu. Let us see how to setup that wondering feature in Internet Explorer.
This a registry tweak and all you have to do is download a small zipped file google.zip which contains the registry file to add the Google search option in you context menu in Internet Explorer, then follow the steps below.
1. Extract the file. It will give two files: google.reg and undo.reg.
2. Double-click on google.reg. Click “Yes” at the “User Account Control” message then again click “Yes” to confirm that you are going to add the registry entry in your computer registry.
You are done! Go to Internet explorer, select any text, right-click on it then select “Search with Google”.

Note:
1. You can undo the change in your registry by clicking on the file undo.reg.
2. If you apply the first method, then you won’t have to add Google search in your context menu manually. There is an option by default in Internet explorer context menu to search for a selected term in the default search engine of the browser. Hence the second method is only useful while you did not follow the first method.
3. Both of the above method work with Internet Explorer 7 and the later version.
Also read:
1. Optimize Your Search Results Searching Two Engines at the Same Time.
2. Working Algorithm Of Google Search Engine.

even after following these methods i couldn’t list google in manage providers.
This link has simple method to add google as default search engine in ie.
http://ajoeblk.blogspot.in/2012/06/how-to-set-google-as-default-search.html