What Peru was talking about was exporting only a portion of your project: The portion under the work area bar. It sounds to me like you are talking about trimming a specific clip so the trimmed off portions do not appear in the timeline. Is that correct?
When you set the in and out points for the clip, do it before you place the clip on the timeline. Then drag the clip from either the project panel or directly from the source monitor window where you set the in and out points and drop it on the timeline. The portion outside the in and out points will not appear in your timeline.
Dragging the clip from the source monitor creates a subclip. You can create multiple subclips from the same source clip by simply setting the in and out points and dragging the subclip to where you want it to go. You can drag subclips from the source monitor to either the project panel for later use or directly to the timeline.
Once on the timeline, changing the in and out points of the source clip do not affect the clip on the timeline. For clips or subclips on the timeline, you can trim the clip further by draging the handles at either end of the clip or by double clicking the clip which will bring it up in the clip monitor window where you can adjust the in and out points.
Here's a basic video on working with in and out points:
http://www.5min.com/Video/How-to-Assign-In-and-Out-Points-in-Adobe-Premiere-Pro-86619376