We use different variables in that case, since we want {{MATH_247}} to be a function of time, {{MATH_248}}. With this adjustment, we define the accumulation function {{MATH_249}} as follows. {{MATH_250}} Since the integral {{MATH_251}} gives the displacement of the object on the time interval {{MATH_252}}, it follows that {{MATH_253}} where {{MATH_254}} gives the position of the object at the time {{MATH_255}}. If we differentiate this equation with respect to {{MATH_256}}, we get that {{MATH_257}} Since {{MATH_258}}, we have that {{MATH_259}} This is the the First Fundamental Theorem of Calculus!