What is equal to?

The value of the integral $$\int_0^{\infty} e^{-x^2} \, dx$$ is​

What is wrong with the following calculation?

​$$\int_{-1}^3 \frac{1}{x^2} d x=-\frac{4}{3}$$​​

​$$\int_{0}^{\frac{\pi}{4}} \sin^3 \theta \, d\theta = \, ?$$​​