textarea.setBorder(null);
In NetBeans:
1. Click the text area
2. Go to Properties
3. Scroll to Other Properties
4. Go to border then select (No Border)
5. Put this in your constructor:
jScrollPane1.setBorder(null);
This is because NetBeans automatically creates scrollpane to your text area and its border is visible until you set it to null.
6. Run the file to see the result.
It worked for me just fine :)


