Subject to contract between the partners,—

(a) if a partner derives any profits for himself from any transaction of the firm, or from the use of the property or business connection of the firm or the firm name, he shall account for that profit and pay it to the firm;

(b) if a partner carries on any business of the same nature as and competing with that of the firm, he shall account for and pay to the firm all profits made by him in that business.