You need to convert the images from the Corel format to one compatible with the internet, such as JPEG or GIF
Just do a "save as" and select the format you want. JPEGS will have a more acurate color, compared to your original. Simpler graphics can be very happy with GIF and they are a much smaller file size.
It would be a good idea to rename your "save as" files, to make sure you don't mess up your original digital images.
Speaking of file size, Photobucket, Imageshack and others may require you to resize your images if they are too large. I am not familiar with where Painter has these controls, but look around. Again, RENAME the file before you resize them down. Once you make the files smaller, you can NEVER bring them back up to size. Renaming them means that you don't have to mess up your originals.