diff --git a/IntegrationLib.py b/IntegrationLib.py
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+import numpy as np
+
+# This function provides the midpoint quadrature rule.
+def Midpoint( a, b, N, f ) :
+    # [a,b] : inteval
+    # N : number of subintervals
+    # f : fonction to integrate using the midpoint rule
+
+    # size of the subintervals
+    H = (b - a) / N
+ 
+    # quadrature nodes
+    x = np.linspace(a+H/2, b-H/2, N)
+
+    # approximate integral 
+    return H * np.sum( f(x) );
+   
+    
+# This function provides the trapezoidal quadrature rule.
+def Trapezoidal( a, b, N, f ) :
+    # [a,b] : inteval
+    # N : number of subintervals
+    # f : fonction to integrate using the trapezoidal rule
+
+    # size of the subintervals
+    H = (b - a) / N
+
+    # quadrature nodes
+    x = np.linspace(a, b, N+1)
+
+    # approximate integral 
+    return H/2 * ( f(a) + f(b) ) + H * sum( f(x[1:N]) );
+
+# This function just provides the Simpson quadrature rule.
+def Simpson( a, b, N, f ) :
+    # [a,b] : inteval
+    # N : number of subintervals
+    # f : fonction to integrate using the Simpson rule
+
+    # size of the subintervals
+    H = (b - a) / N
+    # points defining intervals
+    x = np.linspace(a, b, N+1)
+    
+    # left quadrature nodes
+    xl = x[0:-1]    
+    # right quadrature nodes
+    xr = x[1:]
+    # middle quadrature nodes
+    xm = (xl+xr)/2
+
+    # approximate integral 
+    return H/6 * sum( f(xl) + 4*f(xm) + f(xr) );