Mathematics

The Fundamental Theorem of Calculus directly connects differentiation and integration: when you take the derivative of an integral with a variable upper limit, the derivative "undoes" the integral and just gives you back the integrand evaluated at that limit. The key is recognizing that $F(x)$ is defined as an accumulation function, so $\frac{dF}{dx}$ asks how fast that accumulated area is growing—which is exactly what $f(x)$ measures at each point.

The Fundamental Theorem of Calculus directly connects differentiation and integration: when you take the derivative of an integral with a variable upper limit, the derivative "undoes" the integral and just gives you back the integrand evaluated at that limit. The key is recognizing that $F(x)$ is defined as an accumulation function, so $\frac{dF}{dx}$ asks how fast that accumulated area is growing—which is exactly what $f(x)$ measures at each point.