Sum of all digits in integers from 10 to 100

To sum the individual digits from 10 to 100, break the computation into standard positional blocks.

First, evaluate the clean grid of 2-digit numbers from 10 to 99 (90 total numbers):

Sum of units digits = 9 × (0 + 1 + 2 + \dots + 9) = 9 × 45 = 405.

Sum of tens digits = 10 × (1 + 2 + 3 + \dots + 9) = 10 × 45 = 450.

Now add the final boundary number, 100: Digits are 1, 0, 0, which adds exactly 1 to the total.

Grand Total = 405 + 450 + 1 = 856.

Answer: (b).