what do you mean by any terminals equally spaced about a zero? and nah there weren't any restrictions
Because a sine curve is symmetrical, the area confined from a zero, say x=0, to another value, say x=a, will be equal to the area from x=-a to x=0. But, since sine changes sign at a zero, one of the areas will be negative, meaning that the areas will sum to zero.
That was probably confusing, but consider one period of a sine curve; both 'halves' are of equal area, but one segment is above the x-axis while the other is below. So when you take the integral over the entire period you get zero.
dx=-\int_{-t}^0\sin(x)dx)
due to symmetry. (You can replace 0 with any other x-intercept.)
Hopefully this is clearer =S