The 'slices' of the x-axis are non-zero:
How can we calculate this area? There are many ways, varying in sophistication, efficiency, and accuracy. The easiest way is to use a Newton-Cotes method of order zero.
That's a fancy way to say, break up the interval into small pieces calculate the value of the function at the location of each piece multiply the width of the piece by its height to find its area add up all the areas...
How small should the intervals be? The smaller you make the pieces, the better the approximation. How small should they be? It depends on your purpose.