jmc

The integers from 1 to 100 that leave a remainder of 1 are 1, 6, 11, $\dots$, 96. If we subtract 1 from each of these numbers, we get 0, 5, 10, $\dots$, 95. If we divide each of these numbers by 5, then we get 0, 1, 2, $\dots$, 19. Finally, if we add 1 to each of these numbers, then we get 1, 2, 3, $\dots$, 20. Therefore, the number of terms in 1, 6, 11, $\dots$, 96 is the same as the number of terms in 1, 2, 3, $\dots$, 20, which is $\boxed{20}$. (This number is the same as the percentage since we are dealing with 100 numbers.)