Clear[f,x,I2]GaussTable={{{"Integration Points"},{"Corresponding Weights"}},{{0},{2}},{{-1/Sqrt[3],1/Sqrt[3]},{1,1}},{{-Sqrt[3/5],0,Sqrt[3/5]},{5/9,8/9,5/9}},{{-0.861136,-0.339981,0.339981,0.861136},{0.347855,0.652145,0.652145,0.347855}},{{-0.90618,-0.538469,0,0.538469,0.90618},{0.236927,0.478629,0.568889,0.478629,0.236927}},{{-0.93247,-0.661209,-0.238619,0.238619,0.661209,0.93247},{0.171324,0.360762,0.467914,0.467914,0.360762,0.171324}}};IG[f_,n_]:=Sum[GaussTable[[n+1,2,i]]*f[GaussTable[[n+1,1,i]]],{i,1,n}];f[x_]:=Cos[x](*function*)h=Sqrt[0.00006*24/2/1]n=Ceiling[2/h]I2[f_,a_,b_,n_]:=(h=(b-a)/n;Sum[f[a+(i-1/2)*h]*h,{i,1,n}])I2[f,-1.0,1,n](*solveintegral*)
0.0268328
75
1.68299