For K-G field, the lagrangian density
$$L=\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{1}{2}m^2\phi^2$$
In ryder quantum field theory book i saw that in next step he writes
$$L=-\frac{1}{2}\phi(\partial_\mu\partial^\mu+m^2)\phi$$
My question is how did we got to second step from first,where did the minus sign came from and how did he pulled out a phi from the derivative in first step?
We can write $\partial_\mu \phi \partial^\mu \phi=\partial_\mu(\phi \partial^\mu \phi)-\phi\partial_\mu \partial^\mu \phi$ by the product rule for differentiation. The term $\partial_\mu(\phi \partial^\mu \phi)$ is a surface term that vanishes when the Langrangian density is integrated over spacetime (under certain assumptions such as the fields decaying fast enough at infinity). This essentially means we can make the replacement $\partial_\mu \phi \partial^\mu \phi \rightarrow -\phi\partial_\mu \partial^\mu \phi$ in the Lagrangian density.
