line_int.c integrate to find area 
Numerical quadrature, x=1 to x=3 

Using trapezoidal method 
f1(x)=x+2.0  np=4,  h=0.666667 
4 function evaluations 
computed area=8, exact area=8, error=0 

f2(x)=x*x+2.0*x+3.0  np=4,  h=0.666667 
4 function evaluations 
computed area=22.8148, exact area=22.6667, error=0.148148 
f2(x)=x*x+2.0*x+3.0  np=8,  h=0.285714 
8 function evaluations 
computed area=22.6939, exact area=22.6667, error=0.0272109 
f2(x)=x*x+2.0*x+3.0  np=16,  h=0.133333 
16 function evaluations 
computed area=22.6726, exact area=22.6667, error=0.00592593 

f3(x)=x*x*x+2.0*x*x+3.0*x+4.0  np=4,  h=0.666667 
4 function evaluations 
computed area=43.8889, exact area=57.3333, error=-13.4444 
f3(x)=x*x*x+2.0*x*x+3.0*x+4.0  np=16,  h=0.133333 
16 function evaluations 
computed area=57.3807, exact area=57.3333, error=0.0474074 
f3(x)=x*x*x+2.0*x*x+3.0*x+4.0  np=64,  h=0.031746 
64 function evaluations 
computed area=57.336, exact area=57.3333, error=0.00268749 

fe(x)=exp(x)  np=4,  h=0.666667 
4 function evaluations 
computed area=32.5898, exact area=17.3673, error=15.2226 
fe(x)=exp(x)  np=16,  h=0.133333 
16 function evaluations 
computed area=17.393, exact area=17.3673, error=0.0257216 
fe(x)=exp(x)  np=64,  h=0.031746 
64 function evaluations 
computed area=17.3687, exact area=17.3673, error=0.00145855 

Using Gauss Legendre method 
f1(x)=x+2.0  np=4 
4 function evaluations 
computed area=8, exact area=8, error=-4.79616e-14 

f2(x)=x*x+2.0*x+3.0  np=4 
4 function evaluations 
computed area=22.6667, exact area=22.6667, error=-1.45661e-13 

f3(x)=x*x*x+2.0*x*x+3.0*x+4  np=4 
4 function evaluations 
computed area=57.3333, exact area=57.3333, error=-3.83693e-13 

fe(x)=exp(x)  np=4 
4 function evaluations 
computed area=17.3673, exact area=17.3673, error=-2.18074e-06 

fe(x)=exp(x)  np=8 
8 function evaluations 
computed area=17.3673, exact area=17.3673, error=-1.20792e-13