  We study an integral equation that extends the problem of
anti-differentiation. We formulate this equation by replacing the classical
derivative with a known nonlocal operator similar to those applied in fracture
mechanics and nonlocal diffusion. We show that this operator converges weakly
to the classical derivative as a nonlocality parameter vanishes. Using Fourier
transforms, we find the general solution to the integral equation. We show that
the nonlocal antiderivative involves an infinite dimensional set of functions
in addition to an arbitrary constant. However, these functions converge weakly
to zero as the nonlocality parameter vanishes. For special types of integral
kernels, we show that the nonlocal antiderivative weakly converges to its
classical counterpart as the nonlocality parameter vanishes.
