jmc

The odd integers between 46 and 64 are 47, 49, $\dots$, 63. These integers form an arithmetic sequence with common difference 2, so the $n^{\text{th}}$ term in this sequence is $47+2(n-1)=2n+45$.

If $2n+45=63$, then $n=9$, so there are 9 such odd integers. The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms, so the sum is $(47+63)/2\cdot 9=\boxed{495}$.