Paints that prevent mildew can be used either inside the home in a bathroom, laundry room or basement, or outside the home like in New Orleans, where moisture in the air has the potential to cause mildew.
Not sure if you need mildew-retardant paint or if that dark patch on wall is dirt? Try this little test: Wearing rubber gloves and eye protection, apply household bleach to the suspected area. Wait five minutes. If the discoloration remains, it was probably dirt. If it disappears, it's likely that the bleach killed mildew. This might be a good spot for mildew retardant paint.
To remove the mildew, add one part household bleach to three parts dish detergent. Scrub, then let the solution sit for 15 minutes and rinse. For serious mildew growth, have the area pressure washed, or use a commercial cleaner available at your local hardware stores. Once the mildew is completely gone, a mildew-retardant paint will keep it away...at least for a while.