Does it hold that for every function $a \in C^\infty(\mathbb{R}^2,\mathbb{R})$ we have $a(x,y) = \int_0^1 \left(a(t\cdot (x,y)) + xt \frac{\partial a}{\partial x}(t \cdot(x,y)) + yt \frac{\partial a}{\partial y}(t \cdot(x,y)) \right) dt$
I am asking this because in an exercise I have tried to solve I managed to get to the right hand side, but I need to reach the left hand side.