Take integral using integration by part

Question

Let us take its integral

$$\int_0^xF(z)dz$$

Note that F() is distribution function.

I used integration by parts.

By I can obtain a trivial result.

I know it’s easy question but I cannot do it.

Integration by parts means That is

I choose u=F(z) then du=dF(z)

dv=dz then z=v

And so on.

Answer 1

In this case you could apply integration by parts in thi way

$$\int_0^xF(z)\cdot 1\,dz=[F(z)\cdot z]_0^x-\int_0^xF'(z)\cdot z\,dz$$