${\int }_{-\pi /4}^{7\pi /4}(\sin x+\cos x)dx=◻$

Step 1 ：Given the integral ${\int }_{-\pi /4}^{7\pi /4}(\sin x+\cos x)dx$, we need to find its value.

Step 2 ：The first step is to find the antiderivative of the function $\sin (x)+\cos (x)$. The antiderivative of $\sin (x)$ is $-\cos (x)$, and the antiderivative of $\cos (x)$ is $\sin (x)$. So, the antiderivative of $\sin (x)+\cos (x)$ is $-\cos (x)+\sin (x)$.

Step 3 ：Next, we apply the Fundamental Theorem of Calculus, which states that the definite integral of a function from a to b is equal to the antiderivative evaluated at b minus the antiderivative evaluated at a.

Step 4 ：We evaluate the antiderivative at $7\pi /4$ and $-\pi /4$ and subtract the two results to find the definite integral. The result is 0.

Step 5 ：This means that the area under the curve of the function from $-\pi /4$ to $7\pi /4$ is 0.

Step 6 ：Final Answer: $\boxed{{\displaystyle 0}}$