means that the integral is with respect to arc length. Imagine if the wire had a uniform mass density - then its mass would clearly be equal to its length times the mass density.
You probably know that the length of a parametrized curve between and is
so . Therefore the integral you are looking for is where is the mass density of the wire at the point . You are told that this is proportional to the distance from the point to the plane, i.e. for some constant . Find the expression for that, substitute it into the integral and then evaluate it.