Indesign problem : background color don't appears in the pdf...

I suggest you try an InDesign forum. You aren't using ExportPDF, which is a special subscription service for people exporting PDF to Word etc.

How did you implement this "background color"?

If, as I suspect, you changed the [Paper] swatch, then you aren't seeing a malfunction. That swatch is non-printing, and will not show up anywhere but in the InDesign editing environment. To add a color in the background, you must actually fill an object with the color and position it behind the rest of the elements in your layout.