find *integral sign with 3pi/2 at the top and -pi/2 at the bottom* (1+sintheta)dtheta

Answer 1

∫_{(-π/2 to 3π/2)} [1 + sinθ]dθ = [θ - cosθ]_{(from -π/2 to 3π/2)}

= [3π/2 - 0] - [-π/2 - 0] = 2π

Answer 2

The antiderivative is θ+cos θ.

You plug in the limits of integration to get the answer.