In this paper on page 8 the author claims that the Taylor expansion for the expression $e^{tD_V}$ where $D_V$ is the Lie derivative with respect to a vector field $V$ (defined by $(D_VG)(x) = \frac{d}{dt}|_{t=0}V(\phi^t_V(x))$ and $\phi^t_V(x)$ is the flow of the differential equation $\dot{\psi} = V(\psi)$ looks like this

$$e^{tD_V} = I +tD_V +t^2\int_0^1(1-\theta)e^{\theta t D_V}D_V^2 d\theta $$

I can't wrap my head around the remainder term. Shouldn't it be of third oder in $D_V$ because the integrand involves the third derivative of the exponential? I was thinking that a change of variables is performed but it didn't work. A related question might be this which is concerned with the same paper but ask a different question, still.