google search in my website

Is it legal to use the google search results in my own website not using the google custom search that google provides?

I have 2 different cases:

The first is that I design a search box, with a google logo and provide options so the user selects which type of content (web, images, videos...), and the the results open in a new window with the normal google search results page. it means I submit the the search query from my website to the google search results.

The second is that I design both the search box and the results page so that the results are shown in my 开发者_如何学运维website instead of the google search results page. I found an example for this: http://demo.tutorialzine.com/2010/09/google-powered-site-search-ajax-jquery/search.html

NB: In both of the cases I will include a google logo and link to the original google.com website as credit.

So which of the two cases or are they both legal?

Thanks.

You may be able to use the Google AJAX API for your purposes. See:

Am I allowed to use the Google AJAX Search API on my site?

Google also provides documentation for developers and example code.

For the legality of specific uses, you should refer to Google AJAX Search API Terms of Use and a lawyer. Good thing you said you don't want to use custom search, because the Google Custom Search Terms of service seem to specifically exclude using it with new windows and within frames in sections 1.4(b) and 1.4(c).