First, just to check, I write what I think and let me know if I am wrong: The definite integral of a function gives us a number whose geometric meaning is the area under the curve between two limiting points. We can calculate this integral as the limit of the sum of the rectangles and the integral symbol means a sum over all rectangles. The indefinite integral of the function f(x) is the function primitive F(x) whose derivative is f(x), and here we are using the fundamental theorem of calculus. Why do we use the same symbol? My question is, How could we calculate the indefinite integral without the fundamental theorem? Could we try it using the definite integral between the limits 0 and x? From a geometric point of view, How could we talk about the indefinite integral? Thanks!!!!!!