An integral is a linear operator. You can move any multiplicative constant inside or outside of the integral.
Suppose you write t as:
tmax + (t - tmax)
tmax = max(t)
Does this help you? It should. Try substituting into your expression. What will happen? Look carefully.
y = exp(-(tmax + (t-tmax))).*cumtrapz(t,(exp(tmax + (t - tmax)).*x));
remember. tmax is a constant. What is
Hint: exp(0) = 1
That lets you reduce the problem a bit:
y = exp(-(t-tmax)).*cumtrapz(t,(exp(t - tmax).*x));
Since t-tmax is now never larger than 0, exp(t-tmax) is never a large number.