Suppose we define the definite integral using the following formula $\int_a f(x) d x=\frac{b-a}{2}(f(a)+f(b))$, for more accurate result for $c \in(a, b) F(c)=\frac{c-a}{2}(f(a)+f(c))+\frac{b-c}{2}(f(b)+f(c)) \quad$. When $c=\frac{a+b}{2}, \int_a^b f(x) d x=\frac{b-a}{4}(f(a)+f(b)+2 f(c))$.
$\int_0^{\pi / 2} \sin x d x$ is equal to