calculus - Substitution Rule for Definite Integrals

I'm working on an integration by parts problem, and I'm trying to substitute to simplify the equation:

$$\int_\sqrt{\frac{\pi}{2}}^\sqrt{\pi} \theta^3 \cos(\theta^2) d\theta$$

Using the substitution rule for definite integrals, I substitute $\theta^2 = t$ and apply the same to the limits of integration:

$$\int_\frac{\pi}{2}^\pi t^\frac{3}{2} \cos(t) dt$$

However, Wolfram|Alpha tells me that I have done something wrong, as these two integrals are not equivalent. Where did I screw up?