Answer
$\int^1_0B(t)dt=\begin{bmatrix}
-7 & \frac{1}{3}\\
\frac{11}{2} & \frac{11}{4} \\
\frac{3}{2} & \frac{2}{\pi} \\
e-1&\frac{3}{4}
\end{bmatrix}$
Work Step by Step
$\int^1_0B(t)dt$ is the integral of the matrix $B(t)$
$\int^1_0B(t)dt=\begin{bmatrix}
\int^1_0 -7 & \int^1_0t^2\\
\int^1_0 (6-t) & \int^1_0 (3t^3+6t^2)\\
\int^1_0(1+t) & \int^1_0 \cos(\frac{\pi t}{2})\\
\int^1_0 e^t & \int^1_0(1-t^3)
\end{bmatrix}=\begin{bmatrix}
-7 & \frac{1}{3}\\
\frac{11}{2} & \frac{11}{4} \\
\frac{3}{2} & \frac{2}{\pi} \\
e-1&\frac{3}{4}
\end{bmatrix}$
