inverse fourier Transformation

clc
close all
clear all
w=-10:0.1:10
t1=-10:0.1:10
x=1./(1+w.^2)
subplot(1,2,1)
plot(w,x)
m=1
for t=-10:0.1:10
    i=1
    sum=0
    for w=-10:0.1:10
        dw=0.1
        sum=1/(2*pi)*(sum+((x(i).*(exp(j*w*t).*dw))))
        i=i+1
    end
        X(m)=sum
        m=m+1
end
y1=abs(X)
t=-10:0.1:10
subplot(1,2,2)
plot(t1,y1)