Strange vector valued integral notation

Question

Let $f:\mathbb R^d\to\mathbb R$ be Lebesgue integrable. How would we define the integral $$I=\int_\mathbb{R^d}xf(x)dx$$ when we require that the integral is itself an element of $\mathbb R^d$? I came across this notation in notes on machine learning theory, and I am not really sure how they want this integral to be defined and calculated. My best guess is that it is a version of the Bochner integral, and we would calculate it component wise as follows: $$\pi_iI=\int_\mathbb{R^d}x_if(x)dx=\int_\mathbb{R}\dots\int_\mathbb{R}x_if(x)dx_1\dots dx_d.$$ Confirmation or the correct interpretation would be much appreciated.