Preheat oven to 375 degrees F (190 degrees C). Lightly grease and flour a 9x5 inch loaf pan.
In a large bowl, stir together flour, baking soda, cinnamon, nutmeg and white sugar. Stir in eggs, applesauce, bananas and vanilla extract. Fold in raisins and nuts if desired. Pour batter into prepared pan.
Bake in preheated oven for 45 to 60 minutes, until a knife inserted into center of the loaf comes out clean.