I had some help to improve the interface little more. http://mathematica.stackexchange.com/questions/113254/correcting-problems-with-the-controls-in-a-manipulate/113404#113404 Yes I know I am posting questions in both forums but I think it is not cheating ;)

So here what final code looks like but there are still some stuff that I would like figure out.

Manipulate[
  DynamicModule[{f = Sin[x], xR = 1, xL = 0, 
    Res = 0.4596976941318603}, Column[
    {Style["1D Definite Integral Calculator", "Function"],
     Row[{"Lower Limit ", InputField[Dynamic[xL], Number]}, Spacer[5]],
     Row[{"Upper Limit ", InputField[Dynamic[xR], Number]}, Spacer[5]],
     Row[{"Function  ", InputField[Dynamic[f]]}, Spacer[20]], 
     Button[Style["Calculate", Green, Bold], 
      Dynamic[Res = 
         NumberForm[
          NIntegrate[f, {x, xL, xR}, WorkingPrecision -> nw], np];]], 
     Row[{"Result", InputField[Dynamic[Res]]}, Spacer[5]], 
     If[fp == True, 
      InputField[
       Dynamic[Plot[f, {x, xL, xR}, Dynamic[PlotLabel -> f]]], 
       FieldSize -> {30, 15}]],
      Button[
      Mouseover[Style["http://www.wolfram.com", "Hyperlink"], 
       Style["http://www.wolfram.com", "HyperlinkActive"]], 
      NotebookLocate[{URL["http://www.wolfram.com"], None}], 
      Appearance -> None]
     },

    ]], {{fp, True, "Plot the function"}, {False, True}, Checkbox, 
   ControlPlacement -> Bottom}, {{np, 16, "NumberFormat"}, 5, 30, 1, 
   ControlPlacement -> Bottom}, {{nw, 16, "WorkingPrecision"}, 10, 30,
    1, ControlPlacement -> Bottom}]]

The problems I would like to solve are: 1- Even though in the DynamicModule (at the beginning) I defined Res=0.4596976941318603 but I can't see all the digits in the panel 2- I could not able to adjust the plot size as I am able to do the fieldsize. Also when I change the function and return the plot is updated. I prefer plot is updated with Calculate button but till now I could not figure that out. 3- InputFields for xR and xL supposed to only get numeric values and incase user inputs character the field should not updated (according to help document) but that is not the case.

Hopefully this little toy problem is helping others too.

Here is a solution that I found for naming the inputfields

Manipulate[
  DynamicModule[{f = Sin[x], xR = 1, xL = 0, Res = 0.4596976941}, 
   Column[{
     Style["Lower Limit:", "Function"], 
     InputField[Dynamic[xL], Number],
     Style["Upper Limit:", "Function"], 
     InputField[Dynamic[xR], Number],
     Style["Function:", "Function"], InputField[Dynamic[f]],
     Style["Result:", "Function"], InputField[Dynamic[Res]], 
     Button["Calculate", 
      Dynamic[Res = 
         NumberForm[
          NIntegrate[f, {x, xL, xR}, WorkingPrecision -> nw], np];]], 
     Dynamic[If[fp == True, Plot[f, {x, xL, xR}]]]}]],
  {{np, 10, "NumberFormat"}, 10, 30, 1, ControlPlacement -> Bottom},
  {{nw, 16, "WorkingPrecision"}, 10, 30, 1, 
   ControlPlacement -> Bottom},
  {{fp, True, "Plot the function"}, {False, True}, Checkbox, 
   ControlPlacement -> Bottom}]]

But I still don't know how to fix the "Null" when I dont want the plot and also even though I specify the inputfields for xL and xR I get an error when I put down a character. According to help document this should not happen.