While we often hear about the government in Beijing claiming the island as the sovereign territory of the Peoples Republic of China (PRC), we don't hear much about the claims made by the government in Taipei that the mainland is the sovereign territory of the Republic of China (ROC).
Although both sides dispute who is the sole legitimate government of a single China, they both agree that territorially it includes the island of Taiwan. Meanwhile, a recent poll suggests that for people on the ground, opinion is divided.[2]
[1] https://en.wikipedia.org/wiki/One-China_policy
[2] http://www.taipeitimes.com/News/taiwan/archives/2013/04/30/2...