nope, no fishing allowed
The turtle you posted eurodoc appears to be a Cooter. It's not a red belly, but the pic isn't clear enough for me to tell which variety it is.
Here's a great taxonomy chart to figure out which type of Cooter it is:
http://www.geocities.com/turtlestevesplace/turtle/guide/13.html
It's also possible that you have a Red-Eared-Slider or a Yellow-Bellied-Slider - people sometimes mistake them for Cooters. A Red-Eared Slider has a distinctive red stripe over it's ear (the turtles in the pic I posted are RES). A Yellow Bellied Slider has a yellow "S" marking on the side of it's head, and a yellow "arrow" marking on it's forehead that comes down and "points" to its nose, like my little YBS, Cash:
Here's a link to a caresheet for Cooters (for the red-belly, but care is the same for all the varieties)
http://www.austinsturtlepage.com/Care/cs-flredbelly.htm
And a link to a caresheet for RES
http://www.austinsturtlepage.com/Care/caresheet-red_ear_slider.htm
Finally, a link for YBS caresheet
http://www.austinsturtlepage.com/Care/cs-yellowbelly.htm
Turtles actually need a lot of special care and can hide illness for a LONG time. Please make sure to read up and give your turtle what he needs. The right diet, the right size habitat, the right temperatures, the right lighting, a basking spot, etc.
www.turtleforum.com is a GREAT place for info and advice.