Relationship Between Differentiation and Integration

Since the derivative of a constant is zero, the arbitrary constant disappears upon differentiation of an antiderivative.

According to the Fundamental Theorem of Calculus, if $F(x)$ is an antiderivative of $f(x)$, then differentiating $\int_a^x f(t)\,dt$ yields $f(x)$.

Differentiation and integration are inverse processes up to an arbitrary constant.

If $F(x)$ is an antiderivative of $f(x)$, then $\frac{d}{dx}[F(x)+C] = f(x)+C$.