Overprint is only present in Indesign when the colour black is used. For black texts it is advisable to enable overprint during printing, so that a small shift on the printing sheet does not immediately lead to white edges.
However, in fully black areas, overprinting can produce undesired results. You can see that when you save this file as a PDF.
Because you have used the default colour black for this area, Indesign will automatically set it to overprint. This will cause the background to partially show through the black area.
You can solve this by going to your swatches, clicking the default black, and choosing a new swatch. Indesign will now make a copy of the original black, which will not automatically be set to overprint. Thus for texts you can use the regular colour black, and for text boxes you can use the copy.
Now click the text box and choose for the copied black to convert the text box. If you now save the file as a PDF, you can see the overprint has been removed.
The black area you have now made is plain black, but you can choose to make it deep black within your swatches for an even better-looking result. You can do this by for example adding 30% Cyan, Magenta and Yellow.
There, now you have removed overprint from your Indesign file.
Are you still having trouble, or do you have other questions? Then check our online help centre, or contact us. We would love to help you.