Effects of horizontal scaling on area under curve?

Question

If f(x) is a continuous function and we stretch it horizontally by a factor n (multiply x by 1/n in the formula) then my intuition and some examples i solved tell me that if we look at a segment of the curve before stretching that covers the domain [a , b], that segment of the curve after stretching will cover the domain [na , nb] and the area under that segment of the curve will be multiplied by n. Is that assumption correct? In short how does streching a curve horizontally by a factor n affect the area under the curve?