Answer
2
Work Step by Step
Use the table "Basic Integration Rules", p.246
$\displaystyle \int x^{n}dx=\frac{x^{n+1}}{n+1}+C, n\neq-1$,
$\displaystyle \int\cos xdx=\sin x+C$,
apply the Fundamental Theorem of Calculus
-----------------
$\displaystyle \int_{-\pi/2}^{\pi/2}(2t+\cos t)dt$
$=[t^{2}+\sin t]_{-\pi/2}^{\pi/2}$
$=(\displaystyle \frac{\pi^{2}}{4}+1)-(\frac{\pi^{2}}{4}-1)$
$=2$
Check: using desmos.com (see image below)
