Curvature difference formula ($F_{\nabla +a}=F_{\nabla }+d_{\nabla }a+a\wedge a$)

If two objects ${\nabla }_1$ and ${\nabla }_2$ are each a connection on a vector bundle and satisfy ${\nabla }_1={\nabla }_2+a$ for an $\mathrm{End}(E)$-valued one-form $a$, thenThis follows by expanding $({\nabla }_2+a{)}^2$ with the covariant exterior derivative on the endomorphism bundle connection.