Im reading Evans PDEs second edition.
On page 28 Theorem 6, we are proving that if $u\in C(U)$ and satisfies the mean-value property for each ball $B(x,r) \subset U$ then $$u\in C^{\infty}(U)$$
Now before I ask my question let me clear some things up: $\eta$ is the standard molifier, and $\eta_{\epsilon}(x)=\frac{1}{\epsilon^{n}}\eta(\frac{x}{\epsilon})$, and lastly $n\alpha(n)r^{n-1}$ is the volume of $dB(0,r)$
In the last step of the proof we use that $$\int_{0}^{\epsilon}\frac{1}{\epsilon^{n}}\cdot\eta(\frac{r}{\epsilon})\cdot n\alpha(n)r^{n-1}dr=\int_{B(0,\epsilon)}\eta_{\epsilon}(y)dy$$
What change of variables is going on ?
EDIT 1 :
Following the advice of a comment, could I add in the step
$$\int_{0}^{\epsilon}\frac{1}{\epsilon^{n}}\cdot\eta(\frac{r}{\epsilon})\cdot n\alpha(n)r^{n-1}dr=\int_{0}^{\epsilon}\frac{1}{\epsilon^{n}} (\int_{dB(0,r)} \eta(\frac{x}{\epsilon})dS(x) ) dr =\int_{B(0,\epsilon)}\eta_{\epsilon}(y)dy$$