Show that T is a regular distribution

Question

I am given a Distribution $$T:D(\mathbb{R}) \rightarrow \mathbb{C}$$ and need to show that it is in fact a regular distribution. Let $T(\varphi)=\varphi(-1)+\varphi'(1)$.
How can I show that this is in fact a regular distribution ? By definition I would need to find a locally integrable function $u$, such that $$\int_{\mathbb{R}}{u(x)\varphi(x)dx = T(\varphi)} \; \text{ for all } \varphi \in D(\mathbb{R}) $$

I would appreciate a hint as I am stuck.

Answer 1

I don't think such a function $u$ exists. The support of $T$ is contained in $\{-1,1\}$ and there is no non-zero locally integrable function with finite support.