Income Elasticity of Demand vs. shift in demand curve I've just read an econ textbook and want to verify a statement/definition about income elasticity of demand.

Changes in income shift the demand curve, and we can measure the responsiveness of demand to income changes by calculating income elasticity of demand as follows:



Question: Where does this change in quantity demanded come from? Is it from a movement along demand curve, or from a shift of demand curve?
Short answer:

Denoting income by $I$, price by $p$, the demand function by $D(I,p)$ and income elasticity of demand by $\eta$, the definition of point elasticity of income is

$$
\eta = \frac{\text{d}D(I,p)}{\text{d}I}\frac{I}{D(I,p)}.
$$

So the change in demand comes from a change in income.

Long answer:

Without specifying your coordinate system the terms "movement along the curve" and "shift of the curve" are meaningless.

Consider the function $f(a,x) = a/x$. Suppose this function determines the value of a variable $y$, that is $y = f(a,x)$. Given $a$ we can plot $f(a,x)$ in the $(x,y)$ coordinate system. If $x$ changes there is movement along the curve in this coordinate system. If $a$ changes the curve shifts in this coordinate system.
However treating $a$ as a variable and given $x$ we could also plot $f(a,x)$ in the $(a,y)$ coordinate system. Then change in $a$ would mean movement along the curve and change in $x$ would shift the curve.

As quantity demanded usually depends on both income and price, you face a similar situation, where $q = D(I,p)$. Income elasticity examines a change in income, but without specifying if your curve is ploted in $(p,q)$ or $(I,q)$ you cannot classify the change in $I$ as either "movement along the curve" or "shift of the curve".