1. definite integrals

$
\int_0^{\pi/2} ( sin4 \theta - cos4 \theta)~d\theta
$

$
\int_1^2(15x^3+e^2x-\frac{4}{x})dx
$

2. Well the integral of $sin(4\Theta)$ is $-\frac{1}{4}cos(4\Theta)$

And the integral of $-cos(4\Theta)$ is $-\frac{1}{4}sin(4\Theta)$

Does that help with the first one?