The demand function for a certain make of replacement cartridges for a water purifier is given by:

p=-0.01x^2-0.1x+6

where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand.

Determine the consumers' surplus if the market price is set at $4/cartridge.

I know the answer is $11,667. How did they get this answer? Particularly, how would I find x for the bounds when I integrate? Please show steps in a thorough, understandable manner.

(The problem involves integration.)

Thank you.

(If anyone asks for a supply function or any second equation -- there is none. This is how the question has been exactly written in the book.)