When I can't choose between two ways of doing something, it usually means both are in fact useful. So, as a compromise, in terms of pure API, I would define it this way:

public Project GetProjectPart(int ProjectId, int firstPartIndex, int lastPartIndex) { }

You can decide not to implement the handling of fistPartIndex & lastPartIndex in the initial phases of your project, but at least the API will be future proof, which I think is a very important part of the decision when I start defining public services.