API Not Give any data ( date filter wont work )

it is because Work object has not a creationDate or updateDate (when the input was done).
It only has a work date.
API has to be changed in order to give result for this request.
It must be noticed that due to specificity of this item, result will not be "all the work elements changed between dates" but "all the work elements defined for dates between dates".
For instance, in your request, if you entered on 2015-04-25 some work for 2015-04-20 (late input) you won't retrive this input. You will retrieve all work for corresponding dates, even if input is done on 2015-05-01.

Ticket #1879 recorded.

Possibly define a filter for work directly in the database, but this is not easy.
Work has been introduced in API in V5.1 (quite late compared to other object) because it is a specific object.
Not all features are available on Work in the API.
Request will be taken into account asap.