The sum of all the odd integers between 1 and 10 is 25.
To calculate this, we first identify all the odd integers between 1 and 10. These are 1, 3, 5, 7, and 9.
Next, we add these numbers together:
1 + 3 + 5 + 7 + 9 = 25
Therefore, the sum of all odd integers between 1 and 10 is indeed 25.