Partial derivative of integral vs. integral of partial derivative

Question

Does the followig equation hold?

$$\frac{{{\partial ^2}}}{{\partial {x^2}}}\left( {\int_{t - h}^t {{x^T}\left( \tau \right)\;W\;x\left( \tau \right)\;d\tau } } \right)\;\mathop = \limits^? \;\;\int_{t - h}^t {\frac{{{\partial ^2}}}{{\partial {x^2}}}\left( {{x^T}\left( \tau \right)\;W\;x\left( \tau \right)\;} \right)d\tau } $$