MATLAB：符号表达式，逆傅里叶变换的积分

Question

我有以下脚本：

clear all; close all;

syms t w

% I seek the Fourier Transform of following f 
f = (heaviside(t+1)-heaviside(t-1))*1 ;
L = 10;

h = ezplot(f,[-L,L]) % plot function of problem
set(h, 'Color','r','LineWidth',4)     
grid on

% seek Fourier Transform fw
fw = int(f * exp(-j * w * t),t,-L,L) 
fw_s = simplify(fw,'IgnoreAnalyticConstraints',true);
fw = fw_s
%fw = (2 * sin(w))/w ;this is the result of Fourier Transform

%inverse Fourier Transform ft
ft = (1/(2*pi)) * int(fw * exp(j * w * t),w,-L,L)
ft_s = simplify(ft,'IgnoreAnalyticConstraints',true);
ft = ft_s

Matlab的答案如下：

%ft = (5734161139222659*int((exp(t*w*i)*sin(w))/w, w == -10..10))/18014398509481984

如何强制Matlab答案为f = (heaviside(t+1)-heaviside(t-1))*1，如问题所示。我知道函数ifourier(fw,w,t)中的构建。但是出于教学目的，我想通过使用原始公式来解决。