Given the function $f(x)=6 x^{2}-3 x+1$. Calculate the following values:
\[
\begin{array}{l}
f(-2)= \\
f(-1)= \\
f(0)= \\
f(1)= \\
f(2)=
\end{array}
\]

Step 1 ：Given the function \(f(x)=6 x^{2}-3 x+1\). We need to substitute the given x values into the function and calculate the result.

Step 2 ：For \(f(-2)\), substitute \(-2\) into the function to get \(6(-2)^2 - 3(-2) + 1 = 24 + 6 + 1 = 31\).

Step 3 ：For \(f(-1)\), substitute \(-1\) into the function to get \(6(-1)^2 - 3(-1) + 1 = 6 + 3 + 1 = 10\).

Step 4 ：For \(f(0)\), substitute \(0\) into the function to get \(6(0)^2 - 3(0) + 1 = 0 + 0 + 1 = 1\).

Step 5 ：For \(f(1)\), substitute \(1\) into the function to get \(6(1)^2 - 3(1) + 1 = 6 - 3 + 1 = 4\).

Step 6 ：For \(f(2)\), substitute \(2\) into the function to get \(6(2)^2 - 3(2) + 1 = 24 - 6 + 1 = 19\).

Step 7 ：Final Answer: \[\begin{array}{l} f(-2)= \boxed{31} \\ f(-1)= \boxed{10} \\ f(0)= \boxed{1} \\ f(1)= \boxed{4} \\ f(2)= \boxed{19} \end{array}\]