That substitution gives you a to contend with.

Instead..

Then you can use

This graph does not cross the x-axis as the maximum value of is 1.

The notation you asked about....

That graph crosses the x-axis every 90 degrees,

however it is symmetrical about the x-axis.

As you are integrating from 0 to 360 degrees,

we calculate 4 times the integral from 0 to 90 degrees.

Also we have negative f(t) for and