I did not see a duplicate here so here is my explanation: I am OK with derivation of arc length and even worked out a simple example using a line!
Graph of y =mx + b and plug into equation from the bounds of 0 to 10 and made my slope = 1 . Works great using arc length formula , the length is 10* square root of 2 ! BUT
An integral solves the quadrature for that particular curve so using the integral as an area according to the first theorem of fundamental calculus or the second theorem for that matter don't I end up with an area? But the length of that line certainly isn't an area under a curve, and in this case the curve just happens to be a straight line. I guess I need a little help unifying the two concepts before moving on.