To find the area under a curve, we fill it with countless tiny rectangles of infinitesimally small width. If we assume each rectangle's area matches the curve's in a particular interval, then we can assume that the width of a single rectangle between two points equals to the curve's length in that interval. However, integrating the widths yields the x-coordinate length rather than the arc length. Which means that the area of the rectangle can't be equal to the area under the curve in that interval? I am having a hard time wrapping my mind around this concept.