Evaluate $f(x)=\sin \left(x^2\right)$, and tell whether its antiderivative $F$ is increasing or decreasing at the point $x=-4$ radians.

Step 1 ：First, we need to evaluate the function $f(x)=\sin \left(x^2\right)$ at $x=-4$.

Step 2 ：We substitute $-4$ into the function to get $f(-4)$.

Step 3 ：Next, we need to determine whether the antiderivative $F$ of $f$ is increasing or decreasing at $x=-4$.

Step 4 ：To do this, we find the derivative of $F$, which is $f$. If $f(-4)>0$, then $F$ is increasing at $x=-4$. If $f(-4)<0$, then $F$ is decreasing at $x=-4$.

Step 5 ：We find that $f(-4)$ is approximately -0.288.

Step 6 ：Since $f(-4)$ is negative, this means that the antiderivative $F$ is decreasing at $x=-4$.

Step 7 ：Final Answer: The value of $f(-4)$ is approximately -0.288, and the antiderivative $F$ is $\boxed{{\displaystyle \text{decreasing}}}$ at $x=-4$.