Nice picture.
No, don't give it away for free, the publisher is selling the book and you should sell a license for your image. You could try using the price calculator on
Alamy as a starting point. Just pick any image and price it according to the details given to you by the design studio. There is a
Polish agency with perhaps more relevant prices - choose an RM image to price.
You need to know the book's print run, whereabouts in the book the image is to be used, e.g. cover or inside, and how big, e.g. 1/4 page, 1/2page, whole, double page spread etc. You also need to know where the book is to be sold, ie, do they require rights for just Poland or is the book in English and to be sold in English speaking countries or perhaps worldwide?
When you license the image you should do it on a non-exclusive basis so that you can licence it again. If they want exclusivity, then they will have to pay a whole lot more money. Remember that you are only selling rights to use the image, you are not selling your copyright.
I hope that helps.
Good luck!
David