You can use function: wc_get_page_id( 'cart' ) to get the ID of the page. This function will use the page setup as 'cart' page and not the slug. Meaning it will keep working also when you setup a different url for your 'cart' on the settings page. This works for all kind of Woocommerce special page, like 'checkout', 'shop' etc.
example:
if (wc_get_page_id( 'cart' ) == get_the_ID()) {
// Do something.
}