Preheat the oven to 375°F. Coat muffin pan with cooking spray or oil.
In a large bowl, combine together the flour, ground flax meal, baking powder, salt, and cinnamon.
In a small bowl, whisk together the eggs and yogurt.Whisk in the sugar, oil and apple juice. Add to the flour mixture and stir just until the dry ingredients are moistened.
Stir in the blueberries and grated carrots.
Divide into muffin tins, filling them 2/3 full.
Bake for 20 minutes, or until a wooden pick inserted in the center of a muffin comes out clean.