Incorrect resource handling with combined enumerable and Task-based deferred execution

EnumerableTaskDeferralResourceMishandling.cs

// This won't work
public static IEnumerable<Task<int>> ParseFile(string path)
{
    using (var reader = new StreamReader(path))
    {
        while (!reader.EndOfStream)
        {
            yield return ReadAndParseAsync(reader);
        }
    }
}

private static async Task<int> ReadAndParseAsync(StreamReader reader)
{
    string line = await reader.ReadLineAsync();
    return int.Parse(line);
}