Look at the graph below, let's consider when n = 2 (2 trapezoids are built). Do take note that for each trapezoid, two points are taken from the left-ended value and right-ended value of the subinterval as part of the vertives. The summation of area of all the trapezoids, 12.47 square units.
If you slide the value of n to higher value, you may see that the trapezoids are narrowed down and the estimation of area below the curve is getting nearer to the actual area below the curve.
Betty, Created with GeoGebra