Number of odd integers between 1000 and 9999 with no digit repeated can be found by analyzing the possible digits for each place value.

Digits for thousands place: There are 9 possible digits (1-9), since the thousands place cannot be zero.

Digits for hundreds place: There are 9 possible digits (0-9), excluding the digit chosen for the thousands place.

Digits for tens place: There are 8 possible digits (0-9), excluding the digits chosen for the thousands and hundreds places.

Digits for units place: There are 5 possible digits (1, 3, 5, 7, 9), as an odd number is required.

To find the total number of odd integers, we multiply the number of possibilities for each place value:

Number of odd integers = (9 choices for thousands place) * (9 choices for hundreds place) * (8 choices for tens place) * (5 choices for units place)

Number of odd integers = 9 * 9 * 8 * 5 = 3240

However, this includes numbers with repeated digits. We need to subtract the numbers with repeated digits from the total.

Numbers with repeated digits:
- Numbers with two repeated digits: There are 9 choices for the repeated digit (excluding zero) and 3 choices for the other digit (odd and not equal to the repeated digit), for a total of 9 * 3 = 27 numbers.
- Numbers with three repeated digits: There are 9 choices for the repeated digit (excluding zero) and 2 choices for the other digit (odd and not equal to the repeated digit), for a total of 9 * 2 = 18 numbers.
- Numbers with four repeated digits: There are 9 choices for the repeated digit (excluding zero) and 1 choice for the other digit (odd and not equal to the repeated digit), for a total of 9 * 1 = 9 numbers.

Total numbers with repeated digits = 27 + 18 + 9 = 54

Subtracting the numbers with repeated digits from the total gives us the number of odd integers with no digit repeated:

Number of odd integers = 3240 - 54 = 3186

Therefore, the correct answer is option C) 2240.