1. Give an example of a function that when differentiated, results in the following functions.
$f(x) = -4$
$g(x) = 3x^2$
$h(x) = \sinh x$
$i(x) = \frac{1}{x^2}$
2. Evaluate the following integral of polynomials and powers of $x$.
$\int (x^4 + 3x^2) \, dx$
3. Evaluate the following definite integral.
$\int_0^\pi (3x^3 + \cos(x)) \, dx$