Differentiating using $\frac{d}{dx}$ of an integral of a function as function of $x$ with bounds including functions as function of $t$ We know how how differentiate an integral using the Leibniz theorem, but how can we differentiate such integrals (shown in the image)?


For the first one zero, once you evaluate you will get a function of just x whose derivative with respect to t is just 0. The second one is the exact same as the original example. You can either a) evaluate it out or b) say t=x dt=dx and then evaluate using second fundamental theorem
