If you take 1 + 2 + 3 + 4 + 5 + ... x - 3 + x - 2 + x - 1 + x

And you make a table it looks like a quadratic formula

Now if you make a graph of each part you add it looks like a triamgle made out of rectangles

Now you could increase by smaller and smaller steps each time

And eventually with enough calculus you could find out that a right angle triangle that fits half a rectangle has the same area as half of that rectangle which you already knew

But you could make it really complicated