Incredimail is quite an old email program that allows “better expressing” oneself by help of animations and funny images. This program is closely related to Incredibar (a toolbar, that is causing browser redirections), thus no wonder that IncrediMail changes search providers as well, to mystart.incredimail.com. This is done by providing opt-out checkbox during incredimail instalation process. Although this tactics is legitimate, it is highly annoying.
Incredimail makes money from advertisements, which are displayed in program, search results and start page. The search results are provided by google, however, the advertisements and organic search are blended together to increase the possibility you click on the ads. As I see no use of replaced search page, I recommend not using mysearch incredimail com or incredimail at all.