
I am confused on how to get from the first statement to the second. Getting from the second statement to the third would just a simple case of substituting s=0.
The solution sheet says to use integration by parts on the second statement to get to the top statement, but I'm still unable to obtain the answer after applying integration by parts to back part of the statement.
Here is the solution sheet I have:

I don't quite understand what is happening here. I'd like to know what exactly are they integrating by parts, because it doesn't seem to be the bit at the end of the second statement.
Also my question is same as the one here, except in this post the poster posted the question in such a way that it looks like the first two statements were given and he was trying to prove the third statement using the first one.