  Differential categories axiomatize the basics of differentiation and provide
categorical models of differential linear logic. A differential category is
said to have antiderivatives if a natural transformation $\mathsf{K}$, which
all differential categories have, is a natural isomorphism. Differential
categories with antiderivatives come equipped with a canonical integration
operator such that generalizations of the Fundamental Theorems of Calculus
hold. In this paper, we show that Blute, Ehrhard, and Tasson's differential
category of convenient vector spaces has antiderivatives. To help prove this
result, we show that a differential linear category -- which is a differential
category with a monoidal coalgebra modality -- has antiderivatives if and only
if one can integrate over the monoidal unit and such that the Fundamental
Theorems of Calculus hold. We also show that generalizations of the relational
model (which are biproduct completions of complete semirings) are also
differential linear categories with antiderivatives.
