Answer
$\int A(t)dt=\begin{bmatrix}
t^2\\
t^3
\end{bmatrix}$
Work Step by Step
Given: $A(t)=\begin{bmatrix}
2t\\
3t^2
\end{bmatrix}$
The antiderivative of the matrix function is given by:
$\int^b_aA(t)dt=\int^b_aa_{ij}(t)dt$
Hence here, $\int A(t)dt=\int\begin{bmatrix}
2t\\
3t^2
\end{bmatrix}dt=\begin{bmatrix}
t^2\\
t^3
\end{bmatrix}$
