Aharonov-Bohm Effect and the Berry Phase: gradient of a line integral of a vector field

I need some advice on how to perform the gradient of a line integral of a vector field.

My problem refers to the Aharonov-Bohm Effect as it is discussed in the QM book from David Griffiths, as it follows in the image linked here –> https://imgur.com/lvuBbXJ

I don’t uderstand how the gradient (nabla operator in $R$) is acting on the integral in g. I need more details about that.