Arrange a rack in the middle of the oven and heat to 350°F.
Mix the flour, cinnamon, baking powder, baking soda, salt, in a medium bowl and set aside.

Then combine the eggs, brown sugar, granulated sugar, yogurt, oil,carrot crushed and vanilla in a large bowl. Add the flour mixture. Combine flour mixture with this.

Preheat the oven 375 F. Then Pour the batter into the prepared pan and spread it into an even layer. Bake until a cake tester or toothpick inserted in the center comes out clean, 60 to 65 minutes.