Integrals with u-substitution

Consider taking the integral of the following function:

Notice any issues? Any roadblocks we may run into?

It's easy enough to take the integral of t...

...but sin(t²) is where things get tricky.

We know that the integral of sin(x) is -cos(x)... however the integral of sin(x²) is not as simple as -cos(x²)!

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