In[119]:= f[x_] := 3 (Sin[x] + 2)/(Cos[2*x] + 1.5)
a = 1;
b = 3;
n = 10;
nn = 2*n;
h = (b - a)/nn;
s = f[a] + f[b];
For[j = 1, j < n, ++j,
  s += 2*f[a + 2 j*h] + 4*f[a + (2*j - 1) h];
  ];
s += 4*f[a + (2 n - 1)*h];
s *= h/3
Integrate[f[x], {x, a, b}]

Out[128]= 19.0347

Out[129]= 19.0348