Integral and Integrand Notation

Hi All,

I have a query regarding the attached jpg. I am not sure I understand how the LHS = to RHS.

The book states that the 'integral' is a function of t only so a total derivative is used on LHS, but the 'integrand' is a function of x and t, therefore a partial derivative is used on the RHS.

I have marked in red what I understand to be the integral and integrand.

1) How is the integral a function of t, isnt it a function of x because of the dx in the integral?

Thanks