How do we get to the second line in this integration?

[electronic engineer]

Hello.I actually didn't know exactly how do we get to the second line with this integration.

 

[Defennder]

Integrate this by splitting up the interval on which it is done:

$$\int^L_{-L} f(t) dt = \int^L_{0} f(t) dt + \int^0_{-L} f(-t) dt$$

Then you'll be able to remove the '| |' and integrate it normally. When you're done with the integration, just substitute in the limits and let L approach infinity.