I'm working out a sum out that asks to find P(a < x < b), and the usual way to do that is to calculate F(b) - F(a). This particular sum however adds up F(a) and F(b).
The PDF is:
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I've computed that $F(1/2) = 23/32$ and $F(-1/2) = 8/32$.
This is how I approached the 2 integrations:
Therefore $P(-1/2 \le X \le 1/2) = 15/32 = F(1/2)-F(-1/2)$.