Because you have an overall acceleration, the reading is taking into account all vibration in the frequency range - meaning you don't know much in the way of details. If you don't know the vibration levels at individual frequencies throughout the range, you can't convert from acceleration to velocity. Even if you did know some of the vibration levels at some frequencies, it would be cumbersome to do such a conversion by hand and fraught with inaccuracies due to estimations and not knowing the various phase relationships. Besides if you had the spectrum (the vibration vs frequency plot), then your software could probably do the integration/conversion for you.
regards.. kv