Use the continuity property, if as some point then on for some . And then the integral cannot possibly equal to . When it is not continous just take a single point jump as a conterexample.

The continous case follows from the fundamental theorem of calculus. Again use the same conterexample involving a point jump. The derivative of the integral at the point just is not equal to the original function at that point.2. integral(f(x), a, t) is differentiable and the derivative = f(t)