Ok, could someone please explain this to me, for I have tried to find it on the internet but everywhere (especially the wikipedia) article is written from an analysis point of view. Functionally I would like to know how it works.

I know that

If $\displaystyle I(\theta)=\int_a^{b}f(x,\theta)d\theta$

That by Lebniz

$\displaystyle \frac{dI(\theta)}{d\theta}=\int_a^{b}f(x,\theta)dx$

So now here is where I am in the dark, does this imply that lets say we integrate the right hand side and get

$\displaystyle F(\theta)$ (obviously there will be no more x's)[/tex]

Then we have that

$\displaystyle I(\theta)=\int{F(\theta)}d\theta$

So

Like

$\displaystyle \int_a^{b}f(x,5)dx=\int{F(\theta)}d\theta\bigg|_{\ theta=5}$

Please if anyone could enlighten me, I have been curious about this method for a while and cannot seem to find a comprehensible source. So if somone could explain it that would be great.

Mathstud