What is the geometrical difference between a line integral with respect to arc length and between a line integral with respect to a variable?

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From my understanding the geometrical interpretation of a line integral simply is the area under a curve in a multidimensional space. I think this understanding of the geometrical interpretation corresponds to the line integral with respect to arc length, is this correct? What is the geometrical interpretation of a line integral with respect to a variable? If they have the same geometrical interpretation, then what is the difference between the two?