I am having trouble on what is probably a simple step in the proof of Theorem 24.1 in Asymptotic Statistics by Van der Vaart. Let $\int K(y) dy = 1$. The author writes:
$$h^4 \int K(y)y^2 dy \int \int_0^1 K(y)y^2 f''(x-shy)^2(1-s)^2dsdy$$
The integral of this with respect to $x$ is bounded above by:
$$h^4 \Big( \int K(y)y^2 dy \Big)^2 \int f''(x)^2 dx \frac{1}{3}$$
Does anyone know how to derive this bound?
Answer is located here: pg 25 https://repositorio.uniandes.edu.co/bitstream/handle/1992/20184/u672237.pdf?sequence=1&isAllowed=y