How to center TableHeadings?

Questions
1

Dear:

In the example bellow how could I center my TableHeadings without using spaces in the definition of them but just using commands? Could you help me?

f[x_] = x^2;

a = 0;
b = 1;
n = 2^m;
\[CapitalDelta]x = (b - a)/n;
nn = PaddedForm[n, 10];
temp1 = PaddedForm[N[\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(n\)]\(f[
a + \((i - 1)\)*\[CapitalDelta]x]\ \[CapitalDelta]x\)\)], {8,6}];
temp2 = PaddedForm[N[\!\(\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(n\)]\(f[a + i*\[CapitalDelta]x]\ \[CapitalDelta]x\)\)], {8, 6}];
list = Table[{nn, temp1, temp2}, {m, 1, 20}];
TableForm[list, TableSpacing -> {1, 5}, TableHeadings -> {None, {"          n", "   Lower", "   Upper"}}]
2

Dear Ana,

 f[x_] = x^2;
 
 a = 0;
 b = 1;
 n = 2^m;
 \[CapitalDelta]x = (b - a)/n;
 nn = PaddedForm[n, 10];
 temp1 = PaddedForm[N[ \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(n\)]\(f[
       a + \((i - 1)\)*\[CapitalDelta]x]\ \[CapitalDelta]x\)\)], {8, 
    6}];
temp2 = PaddedForm[N[\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(n\)]\(f[
       a + i*\[CapitalDelta]x]\ \[CapitalDelta]x\)\)], {8, 6}];
list = Table[{nn, temp1, temp2}, {m, 1, 20}];
TableForm[list, TableSpacing -> {1, 5}, 
 TableHeadings -> {None, {"n", "Lower", "Upper"}}, 
 TableAlignments -> Right]

appears to be doing something similar to what you do with the spaces. The “n” appears to be aligned like you want. The “upper” and “lower” are a bit more to the right, with this automatic choice. You can also use

TableAlignments -> Center

and see whether you like that better. Check also the documentation entry for “TableAlignments”.

M.