The integral’s symbols is an oddly shaped ‘S’ because the purpose of the integral is to sum or add everything between the lower limit and the upper limit. If you sum everything together, that is exactly what the area under the curve is. Imagine you draw a vertical line on the x-axis where the lower limit is. Imagine drawing a vertical line on the y-axis where the upper limit is. The space between these 2 lines is what the integral is going to sum. Hope this helps.