I know it would sound stupid, but I am really confused.

Find the area under y=sinx from -π/2 to π/2. If I plug this into TI-83 calculator, I get 2. Which makes sense to me.

But if I do it by myself, the definite integral ∫sinx dx from -π/2 to π/2. I got zero on it, because the antiderivative of sinx is -cosx, so both the values for π/2 and -π/2 is zero, isn't it.

So this two way of doing this don't match. What's the problem?

Thank you.