original_query: What are the conditions for a function to have a continuous antiderivative?
query: What are the conditions for a function to have a continuous antiderivative?
answer: A function has a continuous antiderivative if it is continuous and has at most one zero.  If there's a zero, the antiderivative should be zero at that point. Otherwise, any antiderivative will suffice. For functions like sine and cosine, where a continuous antiderivative taking the value zero at the roots doesn't exist, a piecewise constant function might need to be added to ensure continuity.