# A simple question about equation of motion in polchinski's String theory?

In page 14 to get the equation of motion, it takes the variation of the action $$S_P[X,\gamma]=-\frac{1}{4\pi\alpha'}\int_Md\tau d\sigma(-\gamma)^{1/2}\gamma^{ab}\partial_a X^\mu\partial_b X_\mu$$ and get the equation (1.2.27) $$\delta S_P=\frac{1}{2\pi\alpha'}\int_{-\infty}^{\infty}d\tau\int_0^ld\sigma(-\gamma)^{1/2}\delta X^\mu\nabla^2X_\mu\\ -\frac{1}{2\pi\alpha'}\int_{-\infty}^{\infty}d\tau(-\gamma)^{1/2}\delta X^\mu\partial^\sigma X_\mu|_{\sigma=0}^{\sigma=l}.$$ He took the coordinate region to be $$-\infty<\tau<\infty, 0\leq\sigma\leq l$$ and said this is a single string propagating without sources.

I cannot understand why he dropped the $$\tau$$ term such as terms $$\partial^\tau X_\mu$$ and only leave the $$\sigma$$ term. Could someone help me?