I'm working through an example following Leibniz rule...but havning trouble following it:

We differentiate:

using Leibniz's Rule:

So just looking at the first integral,

I don't understand the b'(x)f(x,b(x)) part of the rule. Here b(x) = x so b'(x) = 1. But for f(x,b(x)) this would become f(x,x) right? I'm not sure why this is the same as y(x) though??

Thanks in advance!