In a small bowl, scatter the yeast and sugar over ½ cup of warm water. Set it aside for 5 minutes to activate the yeast.
Combine in a mixer 3 ½ cups of flour, salt, yeast and the rest of the water.
In a small bowl, toss the blueberries in ¼ cup of flour. Fold the blueberries into the dough.
Beat the ingredients together until the dough does not stick to the side of the bowl. It should be soft and purple in colour.
Transfer dough to a large bowl and cover with a dish towel set it aside in a warm area for 1 ½ hours.
Push the dough down and transfer to a lightly floured surface. Knead several times before dividing into 8 sections and place on a baking sheet.
Roll the portions into a tube shape, sealing the edges then form them into a bagel shape. Cover with dish towel and let set for 30 minutes.
With 10 minutes left to go, preheat oven to 425 F or 218 C and bring a large pot of water to a boil.
Cook the bagels in the boiling water for 3-4 minutes, making sure to turn them over to bake both sides. Remove the bagels from the water and return to the baking sheet.
Bake the bagels for 20 minutes until they are golden brown.