Answer
$=\begin{bmatrix}
1\\
1
\end{bmatrix}$
Work Step by Step
Given: $A(t)=\begin{bmatrix}
\cos t \\
\sin t
\end{bmatrix}$
The antiderivative of the matrix function is given by:
$\int^b_aA(t)dt=\int^b_aa_{ij}(t)dt$
Hence here, $\int^b_a=\int ^{\frac{\pi}{2}}_0\begin{bmatrix}
\cos t \\
\sin t
\end{bmatrix}=\begin{bmatrix}
\sin \frac{\pi}{2} - \sin 0 \\
-\cos \frac{\pi}{2} - \cos 0
\end{bmatrix}=\begin{bmatrix}
1\\
1
\end{bmatrix}$
