I have several widgets at my right sidebar, but I want to totally remove the border from the last two, which are just banners (text/HTML widgets). Is it possible? How can I do it?

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Go and view the page, then look at the page source. Now find the widgets and you should be able to create a CSS selector for the widget and then the CSS rules to get rid of the border.

If you need help with the CSS selectors or rules I recommend visiting http://www.w3schools.com/css I use them constantly as a reference