python - I have a table of values that I want to integrate with other functions -

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i have table of lot of data points, , want use them function multiply other functions , integrate. i'm not sure how go this. figured out how integrate table using simpsons rule, , tried use numpy.polynomial.plynomial.polyfit best fit curve points values way off here have far: 

import numpy np scipy import stats, integrate import matplotlib.pyplot plt scipy.integrate import quad import math  s=5.670367e-8  a,b=np.array(np.loadtxt('cagn2.txt',  skiprows=1, unpack=true)) #change file  based on agn want. freq=np.arange(1e12,1e24,7e16)    a1=a*2.41798926215e14  def f(nu):     return nu**-1   #changed based on want  def total(nu):     return b * nu* f(nu)  """ here want place function describing data points instead of 'b'"""  e,err=quad(total,0,np.inf) #print(e) =integrate.simps(total,a1,even='first') #integrates table only, not want #print(i)  c1,c2,c3,c4,c5=np.polynomial.polynomial.polyfit(a1,b,4)   def y(x): return c1+ c2*x + c3*x**2+c4*x**3+ c5*x**4 n=y(freq)  ax=plt.gca() ax.set_xscale('log') ax.set_yscale('log') plt.plot(a1,b) plt.plot(freq,n) plt.show()

this graph got, orange polyfit. graph of polyfit

as can see way off. know how can closer fit or how use table directly 'b' in total function? thanks





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