Preheat the oven to 350°F (175°C). Grease a baking pan.
In a mixing bowl, combine the flour, sugar, baking soda, cinnamon, nutmeg, and salt.
In another bowl, mix the pumpkin puree, vegetable oil, and eggs until smooth.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the chopped apples.
Pour the batter into the prepared baking pan.
Bake for 45 minutes or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.