I believe in MATLAB you don't have to declare variables before assigning values to the variable.

I'm going to attempted to break this down, despite not knowing how to program in MATLAB so bare with me.

function y = chfun_heston(s0, v0, vbar, a, vvol, r, rho, t, w);

alpha = -w.*w/2 - i*w/2;
beta = a - rho*vvol*i*w;
gamma = vvol*vvol/2;
h = sqrt(beta.*beta - 4*alpha*gamma);
rplus = (beta + h)/vvol/vvol;
rminus = (beta - h)/vvol/vvol;
g=rminus./rplus;

C = a * (rminus * t - (2 / vvol^2) .* log((1 - g .* exp(-h*t))./(1-g)));
D = rminus .* (1 - exp(-h * t))./(1 - g .* exp(-h*t));

y = exp(C*vbar + D*v0 + i*w*log(s0*exp(r*t))); 

function y = call_heston_cf(s0, v0, vbar, a, vvol, r, rho, t, k)

int1 = @(w, s0, v0, vbar, a, vvol, r, rho, t, k) real(exp(-i.*w*log(k)).*chfun_heston(s0, v0, vbar, a, vvol, r,
rho, t, w-i)./(i*w.*chfun_heston(s0, v0, vbar, a, vvol, r, rho, t, -i))); % inner integral1
int1 = integral(@(w)int1(w,s0, v0, vbar, a, vvol, r, rho, t, k),0,100); % numerical integration
pi1 = int1/pi+0.5; % final pi1