I'm struggling with this: $\displaystyle \frac{d}{dx}\int_{x}^{\pi/2} sin\frac{t}{2}cos\frac{t}{3} \, dt$

Using $\displaystyle \frac{d}{dx}\int_{a}^{g(x)} f(t) \, dt =f(g(x)) g'(x)$, I get $\displaystyle \frac{sin\frac{x}{2}sin\frac{x}{3}}{3}-\frac{cos\frac{x}{3}cos\frac{x}{2}}{2}$, which is wrong (I think).