\[\frac{\mathrm{d}}{\mathrm{d}x}\int^{\beta(x)}_{\alpha(x)}f(x,y)\,\mathrm{d}y={%
f(x,\beta(x))\beta^{\prime}(x)-f(x,\alpha(x))\alpha^{\prime}(x)}+\int^{\beta(x%
)}_{\alpha(x)}\frac{\partial f}{\partial x}\,\mathrm{d}y.\]