The servlet-api.jar does contain HttpServlet, HttpServletRequest and HttpServletResponse.
The problem is in the path, make sure that you are pointing to the right path that contains the mentioned jar above.
HttpServlet, HttpServletRequest, and HttpServletResponse are all in the J2EE library. It may be that you only have Java SE (Java standard edition) installed. Be sure to download J2EE and place the j2ee.jar file in your classpath.
Note: The "javax" in import javax.servlet.* is a sure sign that it is J2EE package.