def sum_of_odd_integers(start, end):
    """
    Counts the sum of all odd integers from start through end, inclusively.

    Args:
        start (int): starting number in range.
        end (int): ending number in range.

    Returns:
        int: the sum of all odd integers from start through end, inclusively.
    """
    if start % 2 == 0:
        start += 1

    sum_of_numbers = 0

    for number in range(start, end+1, 2):
        sum_of_numbers += number

    return sum_of_numbers