What change of variables is this?

I think he is breaking the difference apart and doing a change of variable in one term only, then recombining.

$$\int_{\mathbb R^n}\frac{f(x+tv) - f(x)}{t}\eta(x)\;dx = \int_{\mathbb R^n}\frac{f(x+tv)}{t}\eta(x)\;dx - \int_{\mathbb R^n}\frac{ f(x)}{t}\eta(x)\;dx$$ $$= \int_{\mathbb R^n}\frac{f(x)}{t}\eta(x-tv)\;dx - \int_{\mathbb R^n}\frac{f(x)}{t}\eta(x)\;dx$$ $$= \int_{\mathbb R^n}f(x)\frac{\eta(x-tv)-\eta(x)}{t}\;dx $$